kolmogorov sinai entropy and lyapunov spectra of a hard sphere gas abstract the mixing behavior of a hard sphere gas has its origin in the exponential growth of small perturbations in phase space this instability is characterized by the so called lyapunov exponents in this work we compute full spectra of lyapunov exponents for the hard sphere gas for a wide range of densities and particle numbers by using a recently developed algorithm in the dilute gas regime the maximum lyapunov exponent is found to obey the krylov relation ln a formula exactly derived for the low density lorentz gas by dorfman and van beijeren we study the system size dependence and the effect of the fluid solid phase transition on the spectra in the second part of this work we describe and test a direct simulation monte carlo method dsmc for the computation of lyapunov spectra and present results for dilute hard sphere gases excellent agreement is obtained with the results of the deterministic simulations this suggests that the lyapunov instability of a hard sphere gas may be analyzed within the framework of kinetic theory

structured pseudospectra for nonlinear eigenvalue problems in this paper we introduce structured pseudospectra for nonlinear eigenvalue problems and derive computable formulae the results are applied to the sensitivity analysis of the eigenvalues of a second order system arising from structural dynamics and of a time delay system arising from laser physics in the former case a comparison is made with the results obtained in the framework of random eigenvalue problems

kolmogorov sinai entropy for dilute gases in equilibrium we consider the density expansion of the kolmogorov sinai ks entropy per particle for a dilute gas in equilibrium and use methods from the kinetic theory of gases to compute the leading term for an equilibrium system the ks entropy hks is the sum of all of the positive lyapunov exponents characterizing the chaotic behavior of the gas we compute hks n where n is the number of particles in the gas this quantity has a density expansion of the form hks n5an 2ln n 1b1o n where n is the single particle collision frequency and nis the reduced number density of the gas the theoretical values for the coefficients a and b are compared with the results of computer simulations with excellent agreement for a and less than satisfactory agreement for b possible reasons for this difference in b are discussed s1063 651x 97 06911 0

error estimates for the interpolating moving least squares method in this paper the interpolating moving least squares imls method presented by lancaster and salkauskas is discussed in details the advantage of the imls method is that the meshless method which is constructed based on the imls method can apply the essential boundary conditions directly and easily a simpler expression of the approximation function of the imls method is obtained then the error estimate of the approximation function and its first and second order derivatives of the imls method are presented in one dimensional case in this paper the theoretical results show that if the order of the polynomial basis functions is big enough and the original function is sufficiently smooth then the approximation function and its partial derivatives are convergent to the exact values in terms of the maximum radius of the domains of influence of nodes for the purpose of demonstration some selected numerical examples are given to prove the theories in this paper

a meshless numerical procedure for solving fractional reaction subdiffusion model via a new combination of alternating direction implicit adi approach and interpolating element free galerkin efg method a new numerical algorithm has been investigated for solving time fractional reaction subdiffusion equation the fractional derivative of the considered equation is described in the riemann liouville sense firstly we discrete the temporal dimension of the considered model using a finite difference scheme a central difference scheme has been applied to discrete the first time derivative and then for discretizing the fractional integral term a difference scheme has been employed with convergence order o 1 moreover to achieve a full discretization scheme a type of meshless method has been improved that is known as element free galerkin efg method the efg method for integration uses a background mesh this method is based on the galerkin weak form in which the test and trial functions are shape functions of moving least squares mls approximation since the shape functions of traditional mls lack the kronecker property essential boundary conditions of a boundary value problem can not be directly computed and other methods must be employed for this issue to this end a new class of mls shape functions has been applied that is called shape functions of interpolating mls the new shape function has the mentioned property in the efg method calculating the appeared two dimensional integrals is a basic issue in this research work the alternating direction implicit approach is combined with the element free galerkin method then using the new proposed method the two dimensional integrals on rectangular domain will be changed to simple one dimensional integrals we prove that the new numerical algorithm is unconditionally stable and also we obtain an error bound for the new procedure using the energy method numerical examples are reported which demonstrate the theoretical results and the efficiency of proposed scheme

the numerical analysis of piezoelectric ceramics based on the hermite type rpim in this paper the hermite type radial point interpolation method rpim is applied to analyze the property of piezoelectric ceramics in order to overcome the defects of finite element method in this method the inside and boundary of the problem domain are discreted by a distribution of nodes and then the interpolation function of nodes are constructed to solve the displacement of the evaluation nodes compared with the finite element method it is easier and faster for the hermite type rpim to accurately achieve solution of the local regions in contrast with the existing meshless methods this method would not cause singularity in the process of evaluating the shape function furthermore the shape function of the hermite type rpim has a better stability and it can adapt to any distribution of nodes in addition the accuracy and stability of the method are proved by the numerical simulation

development of a novel meshless local kriging lokriging method for structural dynamic analysis this paper presents a novel meshless approach to study the dynamic responses of structures it is called local kriging lokriging method where the kriging interpolation is employed to construct the field approximation function and meshless shape functions and the local weak form of partial differential governing equations is derived by the weighted residual technique since the shape functions constructed by this interpolation possess the delta function property even for a set of randomly distributed points the essential boundary condition can be easily imposed in implementation of local weak form the spline function with high continuity is used as the weight function no mesh is required either for integration of the local weak form or for construction of the shape functions thus the present lokriging method is a truly meshless method several numerical examinations for the free forced vibrational analysis of structures and the dynamic performance of microelectromechanical systems mems device are carried out to demonstrate the accuracy and efficiency of the lokriging method the numerical results show that the presently developed method is quite easy to implement very accurate and highly efficient for the problems considered

moving least squares approximation with discontinuous derivative basis functions for shell structures with slope discontinuities moving least squares approximation with discontinuous derivative basis functions mlsa dbf is introduced for analysis of shell structures with slope discontinuities to deal with shells with arbitrary slope discontinuities the cartesian coordinate is introduced in the construction of mlsa on the shell surface the possible causes of singularity in the moment matrix of mlsa on the shell surface with slope discontinuities are identified and the moore penrose pseudoinverse is used to obtain the generalized inverse of the singular moment matrix resulting from linear dependency and insufficient influence nodes in the mlsa following the proposed formulations for shear deformable shell structures with slope discontinuities in the cartesian coordinates several numerical examples are analyzed to demonstrate the performance validity accuracy and convergence properties of the proposed mlsa dbf approach

meshless formulations for simply supported and clamped plate problems in this paper simply supported and clamped thin elastic plates are analysed the biharmonic differential equation representing the basis of the kirchhoff theory is decomposed into two poisson equations local boundary integral equations are derived for this system of equations the meshless approximation based on the moving least squares method is employed for the implementation in the case of simply supported plates it is sufficient to use the local boundary integral equations for the case of clamped plates we propose to use a combination of the local boundary integral equations and the global ones then two groups of nodal unknowns are computed separately this leads to a reduced system of algebraic equations copyright 2002 john wiley sons ltd

a meshless local kriging method for large deformation analyses in this paper a well developed meshless numerical technique local kriging lokriging method is used to develop the lokriging formulation for the large deformation problems which are geometrically nonlinear this is the first work for the geometrically nonlinear analyses by this meshless local weak form method in the lokriging method the kriging interpolation is employed to construct the meshless shape functions the spline function with high continuity is used as the weight function the discrete equations of the large deformation analysis for two dimensional solids are obtained using the local weak forms and based on the total lagrangian tl approach the presently developed lokriging method is a truly meshless method as it does not require the mesh either for the construction of the shape functions or for the integration of the local weak form several numerical examples of the two dimensional geometrically nonlinear analysis are presented to illustrate the performance of the present lokriging method the present nonlinear lokriging formulation is also used for the large deformation analysis of the microelectromechanical systems mems device the numerical results are compared with the experimental results very good results are obtained all these applications have demonstrated that the present lokriging method is very effective for the large deformation analyses because it avoids all mesh distortion issues

moving kriging interpolation and element free galerkin method a new formulation of the element free galerkin efg method is presented in this paper efg has been extensively popularized in the literature in recent years due to its flexibility and high convergence rate in solving boundary value problems however accurate imposition of essential boundary conditions in the efg method often presents difficulties because the kronecker delta property which is satisfied by finite element shape functions does not necessarily hold for the efg shape function the proposed new formulation of efg eliminates this shortcoming through the moving kriging mk interpolation two major properties of the mk interpolation the kronecker delta property i s j i j and the consistency property n i i x i and n i i x x l i x i are proved some preliminary numerical results arc given

conditional empirical processes defined by φ mixing sequences for a random vector x y in r 2 let m y x p y y x x be the conditional distribution function it is assumed that x 1 y 1 x 2 y 2 form a strictly stationary mixing sequence of random vectors with the same distribution as x y considering an estimate mn x of m x it is shown that nan 1 2 mn x 0 m x 0 converges to a certain gaussian process depending on x 0 where an is a sequence of bandwiths

differential cubature method for static solutions of arbitrarily shaped thick plates this paper presents the first endeavor to exploit the differential cubature method as an accurate and efficient global technique for fundamental solutions of arbitrarily shaped thick plates the method is examined here for its suitability for solving the boundary value problem of thick plates governing by the first order shear deformation theory using the method the governing differential equations and boundary conditions are transformed into sets of linear algebraic equations boundary conditions are implemented through discrete grid points by constraining displacements bending moments and rotations detailed discussion on the formulation and implementation of the method are presented the applicability efficiency and simplicity of the method are demonstrated through solving example plate problems of different shapes the accuracy of the method is verified by direct comparison with the known values

numerical analysis of biot s consolidation process by radial point interpolation method an algorithm is proposed to solve biot s consolidation problem using meshless method called a radial point interpolation method radial pim the radial pim is advantageous over the meshless methods based on moving least square mls method in implementation of essential boundary condition and over the original pim with polynomial basis in avoiding singularity when shape functions are constructed two variables in biot s consolidation theory displacement and excess pore water pressure are spatially approximated by the same shape functions through the radial pim technique fully implicit integration scheme is proposed in time domain to avoid spurious ripple effect some examples with structured and unstructured nodes are studied and compared with closed form solution or finite element method solutions

the development of variable step symplectic integrators with application to the two body problem the authors develop and test variable step symplectic runge kutta nystrom algorithms for the integration of hamiltonian systems of ordinary differential equations numerical experiments suggest that for symplectic formulae moving from constant to variable stepsizes results in a marked decrease in efficiency on the other hand symplectic formulae with constant stepsizes may outperform available standard nonsymplectic variable step codes for the model situation consisting in the long time integration of the two body problem our experimental findings are backed by theoretical analysis

a meshless multilayer model for a coastal system by radial basis functions abstract a multilayer computational model for simulating three dimensional tidal flows in coastal waters is presented in this paper a truly meshless numerical scheme based on radial basis functions rbfs is employed to obtain an accurate approximation to the solution of the model for computational efficiency in solving large scale problems a noniterative domain decomposition method is combined with the use of the rbfs scheme to smooth the numerical simulation of the advection across each subdomain the commonly used upstream technique is also incorporated finally for numerical verification the proposed multilayer model is successfully used to obtain a stable and convergent simulation of the water flows in the pearl river estuary of the south china sea the numerical approximations exhibit good agreement with the observed tidal and current data

ultrashort self similar solutions of the cubic quintic nonlinear schrodinger equation with distributed coefficients in the inhomogeneous fiber by means of the similarity transformation we obtain exact self similar solutions similaritons of the generalized cubic quintic cq nonlinear schrodinger equation with spatially inhomogeneous group velocity dispersion cq nonlinearity and amplification or attenuation exact balance conditions between the dispersion nonlinearity and the gain loss have been obtained as an example we investigate their propagation dynamics in the dispersion decreasing fiber ddf considering the fluctuation of the fiber parameter in real application the exact balance conditions do not satisfy and so we perform direct numerical analysis with initial 10 white noise for the bright similariton in both the ddf and the periodic distributed amplification system numerical calculations indicate stable propagation of the bright similariton over tens of dispersion lengths these ultrashort self similar optical waves are potentially useful for all optical data processing schemes and the design of beam compressors and amplifiers

moving least squares differential quadrature method and its application to the analysis of shear deformable plates a moving least squares differential quadrature mlsdq method is developed and employed for the analysis of moderately thick plates based on the first order shear deformation theory fsdt to carry out the analysis the governing equations in terms of the generalized displacements transverse deflection and two rotations of the plate are formulated by employing the moving least squares approximation the weighting coefficients used in the mlsdq approximation are computed through a fast computation of shape functions and their derivatives numerical examples illustrating the accuracy stability and convergence of the mlsdq method are presented effects of support size order of completeness and node irregularity on the numerical accuracy are investigated copyright 2003 john wiley sons ltd

unconditionally stable meshless integration of time domain maxwell s curl equations grid based methods coupled with an explicit approach for the evolution in time are traditionally adopted in solving pdes in computational electromagnetics the discretization in space with a grid covering the problem domain and a stability step size restriction must be accepted evidence is given that efforts need for overcoming these heavy constraints the connectivity laws among the points scattered in the problem domain can be avoided by using meshless methods among these the smoothed particle electromagnetics gives an interesting answer to the problem overcoming the limit of the grid generation in the original formulation an explicit integration scheme is used providing spatial and time discretization strictly interleaved and mutually conditioned in this paper a formulation of the alternating direction implicit scheme is proposed into the meshless framework the developed formulation preserves the leapfrog marching on in time of the explicit integration scheme studies on the systems matrices arising at each temporal step are reported referring to the meshless discretization the new method not constrained by a grid in space and unconditionally stable in time is validated by numerical simulations

remediation of contaminated groundwater by meshless local weak forms in this paper four meshless local weak form methods such as direct meshless local petrovgalerkin method dmlpg meshless local petrovgalerkin method mlpg local weak radial point interpolation method lwrpim and local weak moving kriging method lwmk are applied to find the numerical solution of coupled non linear advectiondiffusionreaction system arising in the prevention of groundwater contamination problem a comparison between these methods is done from the perspective of accuracy and computational efficiency an efficient fourth order exponential time differencing rungekutta method is utilized for the time discretization the computational efficiency is the most significant advantage of the dmlpg method in comparison with the other meshless local weak form methods because dmlpg reduces the computational costs significantly this is due to the fact that dmlpg shifts the numerical integrations over low degree polynomials rather than over complicated shape functions the main aim of this paper is to show that the meshless local weak form methods can be used for solving the system of non linear partial differential equations especially coupled non linear advectiondiffusionreaction system the numerical results confirm the good efficiency of the proposed methods for solving our model

low rank differential equations for hamiltonian matrix nearness problems for a hamiltonian matrix with purely imaginary eigenvalues we aim to determine the nearest hamiltonian matrix such that some or all eigenvalues leave the imaginary axis conversely for a hamiltonian matrix with all eigenvalues lying off the imaginary axis we look for a nearest hamiltonian matrix that has a pair of imaginary eigenvalues the hamiltonian matrices can be allowed to be complex or restricted to be real such hamiltonian matrix nearness problems are motivated by applications such as the analysis of passive control systems they are closely related to the problem of determining extremal points of hamiltonian pseudospectra we obtain a characterization of optimal perturbations which turn out to be of low rank and are attractive stationary points of low rank differential equations that we derive we use a two level approach where in the inner level we determine extremal points of the hamiltonian varepsilon pseudospectrum for a given varepsilon by following the low rank differential equations into a stationary point and on the outer level we optimize for varepsilon this permits us to give fast algorithms exhibiting quadratic convergence for solving the considered hamiltonian matrix nearness problems

a mesh free method for static and free vibration analyses of thin plates of complicated shape a mesh free method is presented to analyze the static deflection and the natural frequencies of thin plates of complicated shape the present method uses moving least squares mls interpolation to construct shape functions based on a set of nodes arbitrarily distributed in the analysis domain discrete system equations are derived from the variational form of system equation for static analysis a penalty method is presented to enforce the essential boundary conditions for frequency analysis of free vibration the essential boundary conditions are represented through a weak form and imposed using orthogonal transformation techniques the present efg method together with techniques for imposing boundary conditions is coded in fortran numerical examples are presented for rectangular elliptical polygonal and complicated plates to demonstrate the convergence and efficiency of the present method

a thin plate formulation without rotation dofs based on the radial point interpolation method and triangular cells a formulation for thin plates with only the deflection as nodal variables has been proposed using the generalized gradient smoothing technique and the radial point interpolation method rpim the deflection fields are approximated using the rpim shape functions which possess the kronecker delta property for easy impositions of essential boundary conditions three types of smoothing domains which are also serving as the numerical integrations domains are constructed based on the background three node triangular cells and the generalized gradient smoothing operation is performed over each of them to obtain the smoothed curvatures the generalized smoothed galerkin weak form is then used to create the discretized system equations the essential boundary conditions of rotations are imposed in the process of constructing the curvature field and the translation boundary conditions are imposed as in the standard fem a number of numerical examples including both static and free vibration analysis are studied using the present methods and the numerical results are compared with the analytical ones and those in the open literatures the results show that the present formulation can obtain very stable and accurate solutions even for the extremely irregular background cells

numerical solution of transient heat conduction problems using improved meshless local petrov galerkin method an improved meshless local petrov galerkin mlpg method is presented and applied to calculate the two dimensional unsteady state heat conduction problems in this method the moving kriging interpolation is employed instead of the traditional mls approximation to construct the mlpg shape functions which possess kronecker delta function property and thus make it easy to implement essential boundary conditions and then the heaviside step function is used as the test function over a local sub domain since no mesh is needed either for integration of the local weak form or for construction of the shape functions the presently developed mlpg method is a truly meshless method several examples are performed to illustrate the accuracy and efficiency of the present method a good agreement can be found among the proposed analytical and finite element methods

spectral value sets a graphical tool for robustness analysis in this note we present a method to determine and visualize the set of all complex numbers to which at least one eigenvalue of a matrix a can be shifted by real or complex perturbations of the form a a a d e where d and e are fixed matrices and the unknown disturbance matrix satisfies 0 both real and complex perturbations are studied the graphical method may be considered as an extension of the classical root locus method to multivariable systems and multiparameter perturbations the results are illustrated by various examples

lyapunov instability local curvature and the fluid solid phase transition in two dimensional particle systems abstract we study the relation between the lyapunov spectrum and the multidimensional geometry of the potential energy surface in terms of the distribution of stable and unstable modes for different models for this purpose we determined lyapunov exponents for the so called correlated cell model and its smooth generalization as a function of the density for various energies in the smooth case averaged structural quantities such as the fraction of unstable modes the gaussian curvature and the riemannian curvature were computed and compared to the mechanical instability of the system in the sense of lyapunov a similar analysis was also carried out for 36 disk systems representing various fluid and solid states in all studied cases the most positive lyapunov exponent exhibits a maximum at the phase transition in agreement with results for the fluid solid transition in many particle systems

transient heat conduction analysis using the mlpg method and modified precise time step integration method the meshless local petrov galerkin mlpg method in conjunction with the modified precise time step integration method in the time domain is proposed for transient heat conduction analysis in this paper the mlpg method is often referred to as a truly meshless method because it requires no elements or background cells for either field interpolation or background integration local weak forms are developed using weighted residual method locally from the partial differential equation of transient heat conduction in order to simplify the treatment of essential boundary conditions the natural neighbour interpolation nni is employed for the construction of trial functions moreover the three node triangular fem shape functions are taken as test functions to reduce the order of integrands involved in domain integrals the semi discrete heat conduction equation is solved numerically with modified precise time step integration method in the time domain the availability and accuracy of the present method for transient heat conduction analysis are tested through numerical examples

structured pseudospectra and random eigenvalues problems in vibrating systems this paper introduces the concept of pseudospectra as a generalized tool for uncertainty quantification and propagation in structural dynamics different types of pseudospectra of matrices and matrix polynomials are explained particular emphasis is given to structured pseudospectra for matrix polynomials which offer a deterministic way of dealing with uncertainties for structural dynamic systems the pseudospectra analysis is compared with the results from monte carlo simulations of uncertain discrete systems two illustrative example problems one with probabilistic uncertainty with various types of statistical distributions and the other with interval type of uncertainty are studied in detail excellent agreement is found between the pseudospectra results and monte carlo simulation results

a moving kriging interpolation based meshless method for numerical simulation of kirchhoff plate problems this paper mainly proposes an alternative way for numerical implementation of thin plates bending based on a new improvement of meshless method which is combined between the standard element free galerkin method and one different shape functions building technique the moving kriging mk interpolation is applied instead of the traditional moving least square approximation in order to overcome kronecker s delta property where the standard method does not satisfy obviously the deflection of the thin plates is approximated via the mk interpolation to illustrate this approach numerical analysis is examined in both regular and irregular systems three examples with different geometric shapes of thin plates undergoing a simply supported boundary are performed in addition two important parameters of the present method are also analyzed a good agreement can be found among the proposed analytical and finite element methods copyright 2008 john wiley sons ltd

a meshless method for kirchhoff plate bending problems in this work a meshless method for the analysis of bending of thin homogeneous plates is presented this meshless method is based on the use of radial basis functions to build an approximation of the general solution of the partial differential equations governing the kirchhoff plate bending problem in order to obtain a symmetric and non singular linear equation system the hermite collocation method is used to assess the formulation a series of plates with different boundary conditions are analysed comparisons are made with other results available in the literature copyright 2001 john wiley sons ltd

a meshfree method for transverse vibrations of anisotropic plates a meshfree approach called displacement boundary method for anisotropic kirchhoff plate dynamic analysis is presented this method is deduced from a variational principle which uses a modified hybrid functional involving the generalized displacements and generalized tractions on the boundary and the lateral deflection in the domain as independent variables the discretization process is based on the employment of the fundamental solutions of the static problem operator for the expression of the variables involved in the functional the stiffness and mass matrices obtained for the dynamic model are frequency independent symmetric and positive definite and their computation involves boundary integrals of regular kernels only due to its features the final resolving system can be solved with the classical approaches by using standard numerical procedures to assess the formulation the free vibrations of some anisotropic plates were calculated and the results compared with those obtained using other solution techniques the present results are in good agreement with those found in the literature showing the accuracy and effectiveness of the proposed approach

a point interpolation meshless method based on radial basis functions a point interpolation meshless method is proposed based on combining radial and polynomial basis functions involvement of radial basis functions overcomes possible singularity associated with the meshless methods based on only the polynomial basis this non singularity is useful in constructing well performed shape functions furthermore the interpolation function obtained passes through all scattered points in an influence domain and thus shape functions are of delta function property this makes the implementation of essential boundary conditions much easier than the meshless methods based on the moving least squares approximation in addition the partial derivatives of shape functions are easily obtained thus improving computational efficiency examples on curve surface fittings and solid mechanics problems show that the accuracy and convergence rate of the present method is high copyright 2002 john wiley sons ltd

differential cubature method a solution technique for kirchhoff plates of arbitrary shape a treatment for bending analysis of kirchhoff plates using the differential cubature dc method is presented to the authors knowledge this represents the first known successful application of the dc method to this problem the plates treated are subjected to various combinations of boundary conditions and of arbitrary plate geometry a discussion on the implementation issues is presented and several numerical test examples are included to demonstrate the applicability efficiency and simplicity of the approximate procedures the accuracy of the procedures is verified by direct comparing the present numerical results of different plate shapes with the existing exact analytical solutions 1 and other sources of numerical values

completely integrable nonlinear schrodinger type equations on moving space curves using the lamb formalism we show that some completely integrable homogeneous and inhomogeneous nonlinear schr odinger nls type equations such as derivative nls extended nls higher order nls inhomogeneous nls circularly and radially symmetric nls and generalized inhomogeneous radially symmetric nls equations can be related to certain types of moving helical space curves

the complex structured singular value a tutorial introduction to the complex structured singular value is presented with an emphasis on the mathematical aspects of the based methods discussed here have been useful for analysing the performance and robustness properties of linear feedback systems several tests for robust stability and performance with computable bounds for transfer functions and their state space realizations are compared and a simple synthesis problem is studied uncertain systems are represented using linear fractional transformations lfts which naturally unify the frequency domain and state space methods

a novel radial point interpolation method for thin plates in the frame of absolute nodal coordinate formulation abstract a novel meshless radial point interpolation method rpim for thin plates in the frame of the absolute nodal coordinate formulation ancf is proposed to overcome the limitations of the finite element method fem finite elements such as the reduced order triangle element base on specht s function rte sf and the reduced order rectangle element rre are often used to discretize thin plates in the frame of the ancf but these elements may lead to discontinuity of strains curvatures and element distortions especially when flexible bodies produce large deformations furthermore the rte sf has poor accuracy and low convergence rate while the rre is not suitable for discretization of the plate with an arbitrary shape to overcome above limitations field nodes inside the support domain are used to construct the shape functions of the rpim without using finite elements thus the points of interest such as gauss integral points are generally located in the center of the support domain in which support domains of different points have more overlapped parts common nodes on the other hand the number of interpolated nodes in the rpim case is more than that in the fem case for the same point of interest these characteristics ensure that the shape function of the rpim can describe displacement fields of ancf with the higher order continuity and overcome the limitations of the fem finally the rpim in the frame of the ancf and its advantages are validated by several numerical examples

a meshfree hermite type radial point interpolation method for kirchhoff plate problems a meshfree computational method is proposed in this paper to solve kirchhoff plate problems of various geometries the deflection of the thin plate is approximated by using a hermite type radial basis function approximation technique the standard galerkin method is adopted to discretize the governing partial differential equations which were derived from using the kirchhoff s plate theory the degrees of freedom for the slopes are included in the approximation to make the proposed method effective in enforcing essential boundary conditions numerical examples with different geometric shapes and various boundary conditions are given to verify the efficiency accuracy and robustness of the method copyright 2005 john wiley sons ltd

adaptive meshless centres and rbf stencils for poisson equation we consider adaptive meshless discretisation of the dirichlet problem for poisson equation based on numerical differentiation stencils obtained with the help of radial basis functions new meshless stencil selection and adaptive refinement algorithms are proposed in 2d numerical experiments show that the accuracy of the solution is comparable with and often better than that achieved by the mesh based adaptive finite element method

improved multiquadric method for elliptic partial differential equations via pde collocation on the boundary the multiquadric radial basis function mq method is a recent meshless collocation method with global basis functions it was introduced for discretizing partial differential equations pdes by kansa in the early 1990s the mq method was originally used for interpolation of scattered data and it was shown to have exponential convergence for interpolation problems in 1 we have extended the kansa mq method to numerical solution and detection of bifurcations in 1d and 2d parameterized nonlinear elliptic pdes we have found there that the modest size nonlinear systems resulting from the mq discretization can be efficiently continued by a standard continuation software such as auto we have observed high accuracy with a small number of unknowns as compared with most known results from the literature in this paper we formulate an improved kansa mq method with pde collocation on the boundary mq pdecb we add an additional set of nodes which can lie inside or outside of the domain adjacent to the boundary and correspondingly add an additional set of collocation equations obtained via collocation of the pde on the boundary numerical results are given that show a considerable improvement in accuracy of the mq pdecb method over the kansa mq method with both methods having exponential convergence with essentially the same rates

real perturbation values and real quadratic forms in a complex vector space abstract a sequence of real numbers connected to a complex matrix is introduced it is shown how these real perturbation values can be computed and that they have several properties similar to the singular values the so called real pseudospectra and real stability radii can be computed using the real perturbation values the main result concerns the signature of real quadratic forms in complex vector spaces

meshless local boundary integral equation method for simply supported and clamped plates resting on elastic foundation abstract simply supported and clamped thin elastic plates resting on a two parameter foundation are analyzed in the paper the governing partial differential equation of fourth order for a plate is decomposed into two coupled partial differential equations of second order one of them is poisson s equation whereas the other one is helmholtz s equation the local boundary integral equation method is used with meshless approximation for both the poisson and the helmholtz equation the moving least square method is employed as the meshless approximation independent of the boundary conditions fictitious nodal unknowns used for the approximation of bending moments and deflections are always coupled in the resulting system of algebraic equations the winkler foundation model follows from the pasternak model if the second parameter is equal to zero numerical results for a square plate with simply and or clamped edges are presented to prove the efficiency of the proposed formulation

structured pseudospectra in structural engineering this paper presents a new method for computing the pseudospectra of a matrix that respects a prescribed sparsity structure the pseudospectrum is defined as the set of points in the complex plane to which an eigenvalue of the matrix can be shifted by a perturbation of a certain size a canonical form for sparsity preserving perturbations is given and a computable formula for the corresponding structured pseudospectra is derived this formula relates the computation of structured pseudospectra to the computation of the structured singular value ssv of an associated matrix although the computation of the ssv in general is an np hard problem algorithms for its approximation are available and demonstrate good performance when applied to the computation of structured pseudospectra of medium sized or highly sparse matrices the method is applied to a wing vibration problem where it is compared with the matrix polynomial approach and to the stability analysis of truss structures new measures for the vulnerability of a truss structure are proposed which are related to the distance to singularity of the associated stiffness matrix copyright 2005 john wiley sons ltd

multiquadric method for the numerical solution of a biphasic mixture model a computational algorithm based on the multiquadric method has been devised to solve the biphasic mixture model the model includes a set of constitutive equations for the fluid flows through the solid phase a set of momentum equations for stress strain equilibrium and a continuity equation for the solid phase and the fluid phase the numerical method does not require the generation of mesh as in the finite element method and hence gives high flexibility in applying the method to irregular geometry numerical examples are made to compute the solution of the confined compression problem which approximates the nonlinear response of soft hydrated tissues under external loading the numerical results are compared with spilker s penalty finite element method

free vibration analyses of thin sector plates by the new version of differential quadrature method abstract the new version of differential quadrature dq method is extended to analyze the free vibration of thin sector plates with various sector angles and six combinations of boundary conditions detailed formulations are given various numerical examples are studied comparisons are made with existing analytical and or numerical data numerical results indicate that convergence can be achieved with increasing in number of grid points and accurate results could be obtained with 9 9 gird or even higher grid by using the extended dq method for the cases considered

mesh free radial point interpolation method for the buckling analysis of mindlin plates subjected to in plane point loads in this paper a mesh free approach is employed for buckling analysis of mindlin plates that are subjected to in plane point loads the radial point interpolation method rpim is used to approximate displacements based on nodes variational forms of the system equations are established two step solution procedures are implemented the non uniform pre stress distribution of plate is first obtained using the rpim based on a two dimensional 2d elastic plane stress problem this predetermined non uniform pre stress distribution is then used to compute buckling loads of plate using the rpim based on mindlin s plate assumption the rpim can easily handle any number and location of nodes in the plate domain for a desired computational accuracy without major difficulties in solving the initial stresses and buckling loads numerical examples considered here include circular and rectangular mindlin plates that are subjected to in plane uniform and point loads with different aspect ratios and boundary conditions the present results are validated against the available analytical and numerical solutions copyright 2004 john wiley sons ltd

a combined approach of efgm and precise algorithm in time domain solving viscoelasticity problems in this paper element free galerkin efg method is combined with a precise algorithm in the time domain for solving viscoelasticity problems by expanding variables at discretized time intervals an initial boundary value problem is converted into a series of recurrent boundary value problems which can be conveniently solved by efg efg fe with a self adaptive computing process there is no requirement of iteration for the solution of non linear cases satisfactory numerical results are obtained for both static and dynamical viscoelasticity problems

proper orthogonal decomposition variational multiscale element free galerkin pod vmefg meshless method for solving incompressible navier stokes equation abstract recently because of simplicity of meshless methods they have been employed for solving many partial differential equations one of the meshless methods is element free galerkin technique the element free galerkin is very similar to the finite element method with this difference that the test and trial spaces of efg procedure are shape functions of moving least squares approximation using the mentioned shape functions solving a problem on a complex domain is very simple some researchers proposed several modifications and enriched approaches for improving the element free galerkin method that one of them is variational multiscale element free galerkin procedure up to the best of authors knowledge the element free galerkin method based on the shape functions of moving least squares approximation needs more cpu time than the element free galerkin method based on the shape functions of moving kriging interpolation thus in the current paper we employ the variational multiscale element free galerkin based on the shape functions of moving kriging interpolation also for reducing the cpu time of the presented numerical scheme we use the proper orthogonal decomposition pod approach therefore in the current paper we propose the proper orthogonal decomposition variational multiscale element free galerkin pod vmefg method for solving time dependent incompressible navier stokes equation moreover several test problems are given that show the acceptable accuracy and efficiency of the proposed scheme

numerical study of three dimensional turing patterns using a meshless method based on moving kriging element free galerkin efg approach in this paper a numerical procedure is presented for solving a class of three dimensional turing system first we discrete the spatial direction using element free galerkin efg method based on the shape functions of moving kriging interpolation then to achieve a high order accuracy we use the fourth order exponential time differencing runge kutta etdrk4 method using this discretization for the temporal dimension we obtain an explicit scheme and do not need to solve nonlinear system of equations the efg method uses a weak form of the considered equation that is similar to the finite element method with the difference that in the efg method test and trial functions are moving least squares approximation mls shape functions since the shape functions of moving least squares mls approximation do not have kronecker delta property we cannot implement the essential boundary condition directly also building shape functions of mls approximation is a time consuming procedure because of the mentioned reasons we employ the shape functions of moving kriging interpolation technique which have the mentioned property and less cpu time is required for building them for testing this method on three dimensional pdes we select some equations and system of pdes such as allen cahn gray scott ginzburg landau brusselator models predator prey model with additional food supply to predator several test problems are solved and numerical simulations are reported which confirm the efficiency of the proposed scheme

multi solitonic solutions for the variable coefficient variant boussinesq model of the nonlinear water waves abstract for the nonlinear and dispersive long gravity waves traveling in two horizontal directions with varying depth of the water we consider a variable coefficient variant boussinesq vcvb model with symbolic computation we construct the connection between the vcvb model and a variable coefficient ablowitz kaup newell segur vcakns system under certain constraints using the n fold darboux transformation of the vcakns system we present two sets of multi solitonic solutions for the vcvb model which are expressed in terms of the vandermonde like and double wronskian determinants respectively dynamics of those solutions are analyzed and graphically discussed such as the parallel solitonic waves shape changing collision head on collision fusion fission behavior and elastic fusion coupled interaction

buckling of rectangular mindlin plates subjected to partial in plane edge loads using the radial point interpolation method this paper considers the elastic buckling of rectangular mindlin plates that are subjected to partially distributed in plane edge loadings a numerical algorithm based on the radial point interpolation method rpim is proposed for the solution of such plates the pre buckling stresses are first determined using the rpim based on a two dimensional 2 d elastic plane stress problem the buckling load intensity factors for rectangular plates that incorporate these predetermined pre buckling stresses are then computed via the rpim based on the mindlin plate theory numerical examples of the plates with various boundaries and subjected to different partially distributed in plane edge loadings are presented shear locking of the buckling load is studied the results demonstrate the high accuracy of the proposed rpim

the complex variable meshless local petrov galerkin method for elasticity problems of functionally graded materials this paper proposed the complex variable meshless local petrov galerkin cvmlpg method for the static analysis of functionally graded materials fgms in the presented method the complex variable moving least square cvmls approximation which is established based on the moving least square mls approximation by introducing the complex variable theory is adopted for construction of the field approximation function compared with the conventional mls method the number of the unknown coefficients in the trial function of the cvmls method is less than that of the mls approximation thus higher efficiency and accuracy can be achieved under the same node distributions one advantage of the cvmlpg method for the fgms is that the variations of the functionally graded material properties are simulated by using material parameters at gauss points so it totally avoids the issue of the assumption of homogeneous in each element in the finite element method fem for the fgms some of selected benchmark examples are considered to confirm the validity and accuracy of the proposed method

on a direct bilinearization method kaup s higher order water wave equation as a modified nonlocal boussinesq equation a systematic procedure for the bilinearization of classes of soliton equations is developed with the help of a generalization of bell s exponential polynomials 1934 application of this procedure to kaup s higher order wave equation 1975 discloses several links with other soliton systems in particular it is found that the kaup equation is the modified version of a sech square soliton system which constitutes an alternative to the good boussinesq equation

the complex variable meshless local petrov galerkin method for elastodynamic problems the complex variable meshless local petrov galerkin cvmlpg method is further developed for structural dynamic analyses of two dimensional 2d solids the complex variable moving least square cvmls approximation is used to construct the shape function and the heaviside step function is chosen for representing the test function in the construction of the well performed shape function the trial function of 2d problem is formed with a one dimensional 1d basis function thus improving computational efficiency the governing elastodynamic equations are transformed into a standard local weak formulation and then it is discretized into a meshfree system of time dependent equations which are solved by the standard implicit newmark time integration scheme numerical results obtained from the proposed cvmlpg method are compared with the exact solutions and those of the conventional mlpg method and excellent agreement is achieved

correlation between the kolmogorov sinai entropy and the self diffusion coefficient in simple liquids molecular dynamics simulations were performed for soft and hard sphere systems for number densities ranging from 0 5 to 1 0 and the kolmogorov sinai entropy ks entropy and self diffusion coefficients were calculated it is found that the ks entropy when expressed in terms of average collision frequency is uniquely related to the self diffusion coefficient by a simple scaling law the dependence of the ks entropy on average collision frequency and number density was also explored numerical results show that the scaling laws proposed by dzugutov and by beijeren dorfman posch and dellago can be applied to both soft and hard sphere systems by changing to more generalized forms

the complex variable meshless local petrovgalerkin method for elastodynamic analysis of functionally graded materials as an improvement of the meshless local petrovgalerkin mlpg the complex variable meshless local petrovgalerkin cvmlpg method is extended here to dynamic analysis of functionally graded materials fgms in this method the complex variable moving least squares cvmls approximation is used instead of the traditional moving least squares mls to construct the shape functions the main advantage of the cvmls approximation over mls approximation is that the number of the unknown coefficients in the trial function of the cvmls approximation is less than that of the mls approximation thus higher efficiency and accuracy can be achieved under the same node distributions in implementation of the present method the variations of the fgms properties are computed by using material parameters at gauss points so it totally avoids the issue of the assumption of homogeneous in each element in the finite element method fem for the fgms several numerical examinations for dynamic analysis of fgms are carried out to demonstrate the accuracy and efficiency of the cvmlpg

n fold darboux transformation and solitonic interactions of a variable coefficient generalized boussinesq system in shallow water abstract under consideration in this paper is a variable coefficient generalized boussinesq system for the long weakly nonlinear and weakly dispersive surface waves in shallow water with the aid of symbolic computation n fold darboux transformation n dt is constructed for that system analytic solutions of the system are obtained via the n dt elastic interactions of three bell shaped and periodic bell shaped solitons are obtained fusion interactions and periodic fusion fission interactions of the solitary waves are graphically analyzed which are inelastic

consistency conditions for the influence graphs generalized finite difference method the modeling of physical phenomena is most often conveyed through partial differential equations governing continuous fields computational approaches are used afterwards in order to approximate the solutions to these equations in doing so a discretized version of the initial model must be set up using one of the numerous available methods this paper illustrates how influence graphs weighted digraphs with geometrical attributes may behave in the same way as differential operators in so far as a set of appropriate conditions of consistency are satisfied these conditions are written explicitly for the most often used cases including differential boundary operators on the one hand a consistent neighborhood may be regarded as a generalization of a classical finite difference scheme on the other hand a consistent influence graph is a discrete object modeling a physical behavior as well as its continuous counterpart numerical experimentations address firstly the second order diffusion model and lastly the fourth order kirchhoff theory of plate deflection

meshless local b spline fd method and its application for 2d heat conduction problems with spatially varying thermal conductivity abstract in this paper a new class of meshless methods based on local collocation and b spline basis functions is presented for solving elliptic problems the proposed approach is called as meshless local b spline basis functions based finite difference local b fd method the method was straightforward to develop and program as it was truly meshless only scattered nodal distribution was required hence avoiding at all mesh connectivity for field variable approximation and integration in the method any governing equations were discretized by b spline approximation in the spirit of fd technique using local b spline collocation i e any derivative at a point or node was stated as neighboring nodal values based on the b spline interpolants in addition as b spline basis functions pose favorable properties such as i easy to construct to any arbitrary order degree ii have partition of unity property and iii can be easily designed to pose the kronecker delta property the shape function construction as well as the imposition of boundary conditions can be incorporated efficiently in the present method the applicability and capability of the present local b fd method were demonstrated through several heat conduction problems with heat generation and spatially varying conductivity

correlation between kolmogorov sinai entropy and self diffusion coefficient in simple fluids the relationship between the kolmogorov sinai entropy h mathrm ks and the self diffusion coefficient d is studied for two classical simple fluid systems with purely repulsive potentials one system with a wayne chandler anderson potential and the other with a hard sphere potential numerical simulation data for h mathrm ks and d normalized by the average collision frequency ensuremath nu and the diameter of the particle ensuremath sigma as natural units of time and distance reveal that in the region spanning from normal liquid up to near solidification 0 50l ensuremath rho l 0 93 the kolmogorov sinai entropy has a power law dependeney on the self diffusion coefficient of the form h mathrm ks ensuremath nu ensuremath propto d ensuremath sigma 2 ensuremath nu ensuremath eta in which ensuremath eta is independent of density and temperature

on the optimal shape parameters of radial basis functions used for 2 d meshless methods abstract a radial point interpolation meshless or radial pim method was proposed by authors to overcome the possible singularity associated with only polynomial basis the radial pim used multiquadric mq or gaussian as basis functions these two radial basis functions all included shape parameters although choice of shape parameters has been a hot topic in approximation theory and some empirical formulae were proposed how these shape parameters affect the accuracy of the radial pim has not been studied yet this paper studied the effect of shape parameters on the numerical accuracy of radial pim a range of suitable shape parameters is obtained from the analysis of the condition number of the system matrix error of energy and irregularity of node distribution it is observed that the widely used shape parameters for mq and reciprocal mq basis are not even close to their optimums the optimal shape parameters are found in this paper to be simply q 1 03 and r 1 42 for mq basis and c 0 003 0 03 for gaussian basis

new solitons for the hirota equation and generalized higher order nonlinear schrodinger equation with variable coefficients in this paper multisoliton solutions of the hirota equation with variable coefficients are obtained by the darboux transformation based on the ablowitz kaup newell segur technology as an example we discuss the evolutional behaviour of a two soliton solution in a soliton control fibre system the results reveal that one may control the interaction between the pulses by choosing the third order dispersion parameters d4 and h appropriately meanwhile more generalized forms of bright soliton and dark soliton solutions of generalized higher order nonlinear schrodinger equations ghonlse with variable coefficients are obtained by the extended tanh function method moreover new bright and dark combined solitary wave kink solitary wave and m shaped solitary wave to ghonlse with variable coefficients are firstly reported in this paper especially the term proportional to 1 resulting from the group velocity decides the group velocity and the phase shift of these new solitary waves

variational multiscale element free galerkin vmefg and local discontinuous galerkin ldg methods for solving two dimensional brusselator reaction diffusion system with and without cross diffusion abstract the finite element method fem is one of the basic methods for solving deterministic and stochastic partial differential equations this method is proposed in the 19 decade and after years several modifications for this well known technique such as mortal fem discontinuous galerkin fem extended fem least squares fem spectral fem mixed fem immersed fem adaptive fem etc have been proposed also for improving the accuracy and for considering complex domain shape functions of the moving least squares approximation have been replaced with the traditional shape function of the finite element technique the name of this improved method is element free galerkin efg method which is classified in the category of meshless methods the efg method has been applied for solving many problems in engineering in the current paper we select two numerical procedures that are extracted from fem the discontinuous galerkin approach is a useful technique for solving problems that their exact solutions have discontinuity it should be noted that many enriched ideas have been explained for improving accuracy of efg method in the current paper the local discontinuous galerkin and variational multiscale efg methods are applied for obtaining numerical solution of two dimensional brusselator system with and without cross diffusion the brusselator system is a theoretical model for a type of autocatalytic reaction up to best of authors knowledge the accuracy of the obtained numerical solutions using local discontinuous galerkin method is very related to the used time discrete scheme therefore fourth order exponential time differencing method has been employed for discretizing the time variable also to achieve a full discretization scheme the local discontinuous galerkin finite element method is used moreover several test problems are given that show the acceptable accuracy and efficiency of the proposed schemes

a moving kriging interpolation based element free galerkin method for structural dynamic analysis in this paper a meshfree method based on the moving kriging interpolation is further developed for free and forced vibration analyses of two dimensional solids the shape function and its derivatives are essentially established through the moving kriging interpolation technique following this technique by possessing the kronecker delta property the method evidently makes it in a simple form and efficient in imposing the essential boundary conditions the governing elastodynamic equations are transformed into a standard weak formulation it is then discretized into a meshfree system of time dependent equations which are solved by the standard implicit newmark time integration scheme numerical examples illustrating the applicability and effectiveness of the proposed method are presented and discussed in details as a consequence it is found that the method is very efficient and accurate for dynamic analysis compared with those of other conventional methods

solitonic excitations and interactions in an α helical protein modeled by three coupled nonlinear schrodinger equations with variable coefficients governing the molecular excitations associated with bioenergy transport in an helical protein through the soliton modes three coupled higher order nonlinear schrodinger equations with variable coefficients are investigated via symbolic computation using bell polynomials a bilinear form and backlund transformation are derived for this model furthermore explicit n soliton solutions are constructed in terms of the double wronskian determinant solitonic excitations are found to remain stable against the disorders of the parameters under certain constraints finally propagation characteristics and interactions of the solitonic excitations are discussed soliton amplitudes are related to the energy modulation coefficients and both the soliton properties and energy distribution during the interactions are affected by the inhomogeneity coefficients of the protein with time dependent disorders

modeling of biological population problems using the element free kp ritz method a degenerate parabolic equation arising in the spatial diffusion of biological population is analyzed using the mesh free kp ritz method the mesh free kernel particle estimate is employed to approximate the 2d displacement field a system of discrete equations is obtained through application of the ritz minimization procedure to the energy expressions to validate the accuracy of the results and stability of the present method convergence studies were carried out based on influences of support size and number of nodes effectiveness of the mesh free kp ritz method for biological population model is investigated by numerical examples in this paper the present results were compared with results reported in extant literature and were found to be in good agreement with the literature

multi soliton solutions and a backlund transformation for a generalized variable coefficient higher order nonlinear schrodinger equation with symbolic computation abstract in this paper by virtue of symbolic computation the investigation is made on a generalized variable coefficient higher order nonlinear schrodinger equation with varying higher order effects and gain or loss which can describe the femtosecond optical pulse propagation in a monomode dielectric waveguide a modified dependent variable transformation is introduced into the bilinear method to transform such an equation into a variable coefficient bilinear form based on the formal parameter expansion technique the multi soliton solutions of this equation are obtained through the bilinear form under sets of parametric constraints a backlund transformation in bilinear form is also obtained for the first time in this paper finally discussions on the analytic soliton solutions are given and various propagation situations are illustrated

surfaces generated by moving least squares methods an analysis of moving least squares m l s methods for smoothing and interpolating scattered data is presented in particular theorems are proved concerning the smoothness of interpolants and the description of m l s processes as projection methods some properties of compositions of the m l s projector with projectors associated with finiteelement schemes are also considered the analysis is accompanied by examples of univariate and bivariate problems

types of solutions of the variable coefficient nonlinear schrodinger equation with symbolic computation by using hirota s bilinear method and symbolic computation solutions for a variable coefficient nonlinear schrodinger equation are obtained theoretically it is found that the type of the solutions changes with the different choices of the group velocity dispersion coefficient beta 2 z according to those solutions the relevant properties and features of physical and optical interest are illustrated in addition an effective technique for controlling the shape of the pulses is presented the results of this paper will be valuable to the study of the future development of ultrahigh rate and long distance optical communication systems

fluctuations and the many body lyapunov exponent an ab initio theoretical method is derived for calculating the maximal lyapunov exponent of an n body system obeying hamilton s equations the theory is developed in detail for a dilute gas it shows the lyapunov exponent to be a function of the time integral of the correlation function for fluctuations in the second derivative of the interparticle potential approximately a power frac 1 3 law we apply the theory to a one component plasma and derive the dependence of the lyapunov exponent on a plasma parameter

a meshless local moving kriging method for two dimensional solids abstract an improved meshless local petrov galerkin method mlpg for stress analysis of two dimensional solids is presented in this paper the mlpg method based on the moving least squares approximation is one of the recent meshless approaches however accurate imposition of essential boundary conditions in the mlpg method often presents difficulties because the mlpg shape functions does not possess the kronecker delta property in order to eliminate this shortcoming this approach uses the moving kriging interpolation instead of the traditional moving least square approximation to construct the mlpg shape functions and then the heaviside step function is used as the test function over a local sub domain in this method the essential boundary conditions can be enforced as the fem no domain integration is needed and only regular boundary integration is involved in addition the sensitivity of several important parameters of the present method is mainly studied and discussed comparing with the original meshless local petrov galerkin method the present method has simpler numerical procedures and lower computation cost the effectiveness of the present method for two dimensional solids problem is investigated by numerical examples in this paper

a point interpolation method for two dimensional solids a point interpolation method pim is presented for stress analysis for two dimensional solids in the pim the problem domain is represented by properly scattered points a technique is proposed to construct polynomial interpolants with delta function property based only on a group of arbitrarily distributed points the pim equations are then derived using variational principles in the pim the essential boundary conditions can be implemented with ease as in the conventional finite element methods the present pim has been coded in fortran the validity and efficiency of the present pim formulation are demonstrated through example problems it is found that the present pim is very easy to implement and very flexible for obtained displacements and stresses of desired accuracy in solids as the elements are not used for meshing the problem domain the present pim opens new avenues to develop adaptive analysis codes for stress analysis in solids and structures copyright 2001 john wiley sons ltd

pseudospectra of linear operators if a matrix or linear operator a is far from normal its eigenvalues or more generally its spectrum may have little to do with its behavior as measured by quantities such as an or exp ta more may be learned by examining the sets in the complex plane known as the pseudospectra of a defined by level curves of the norm of the resolvent zi a 1 five years ago the author published a paper that presented computed pseudospectra of thirteen highly nonnormal matrices arising in various applications since that time analogous computations have been carried out for differential and integral operators this paper a companion to the earlier one presents ten examples each chosen to illustrate one or more mathematical or physical principles

pseudospectra and delay differential equations in this paper we present a new method for computing the pseudospectra of delay differential equations ddes with fixed finite delay this provides information on the sensitivity of eigenvalues under arbitrary perturbations of a given size and hence insight into how stability may change under variation of parameters we also investigate how differently weighted perturbations applied to the individual matrices of the delayed eigenvalue problem affect the pseudospectra furthermore we compute pseudospectra of the infinitesimal generator of the dde from which a lower bound on the maximum transient growth can be inferred to illustrate our method we consider a dde modelling a semiconductor laser subject to external feedback

error analysis of a meshless weak form method based on radial point interpolation technique for sivashinsky equation arising in the alloy solidification problem abstract in this paper meshless weak form techniques are applied to find the numerical solution of nonlinear biharmonic sivashinsky equation arising in the alloy solidification problem stability and convergence analysis of time discrete scheme are proved an error analysis of meshless global weak form method based on radial point interpolation technique is proposed for this nonlinear biharmonic equation in addition a comparison between meshless global and local weak form methods is done from the perspective of accuracy and efficiency the main purpose of this paper is to show that the meshless weak form techniques can be used for solving the nonlinear biharmonic partial differential equations especially sivashinsky equation the numerical results confirm the good efficiency of the proposed methods for solving this nonlinear biharmonic model

solitonic solutions and backlund transformation for the inhomogeneous n coupled nonlinear schrodinger equations abstract governing the simultaneous propagation of n fields in optical fibers and plasmas the inhomogeneous n coupled nonlinear schrodinger equations are with symbolic computation analytically investigated in this paper as one of the important integrable properties the explicit one and two solitonic solutions for the inhomogeneous n coupled nonlinear schrodinger equations are derived using the bilinear method with illustrated graphics additionally the backlund transformation in bilinear form is constructed

on the combinatorics of the hirota d operators a generic formula is presented which relates the hirota d operators to simple combinatorics particular classes of partition polynomials bell polynomials and generalizations are found to play an important role in the characterization of bilinearizable equations as a consequence it is shown that bilinear backlund transformations for single field bilinearizable equations linearize systematically into corresponding laxpairs

stability radius for structured perturbations and the algebraic riccati equation abstract in this paper we generalize the notion of stability radius introduced in 1 to allow for structured perturbations we then relate the stability radius to the existence of hermitian solutions of an algebraic riccati equation and give some applications of this result

soliton solutions and a backlund transformation for a generalized nonlinear schrodinger equation with variable coefficients from optical fiber communications under investigation in this paper is a generalized nonlinear schrodinger model with variable dispersion nonlinearity and gain loss which could describe the propagation of optical pulse in inhomogeneous fiber systems by employing the hirota method one and two soliton solutions are obtained with the aid of symbolic computation furthermore a general formula which denotes multi soliton solutions is given some main properties of the solutions are discussed simultaneously as one important property of nonlinear evolution equation the backlund transformation in bilinear form is also constructed which is helpful on future research and as far as we know is firstly proposed in this paper