a complex variable boundary point interpolation method for the nonlinear signorini problem abstract a complex variable boundary point interpolation method cvbpim is presented for numerical analysis of the nonlinear signorini problem to reduce the computational cost and to improve the stability of the point interpolation method a complex variable point interpolation method cvpim is developed to construct meshless shape functions with interpolation properties by using a projection technique to deal with the nonlinear inequality boundary conditions and combining boundary integral equations with the cvpim to establish discrete linear algebraic systems the cvbpim is an easy to implement and boundary only meshless method for nonlinear signorini problems numerical results are presented to show the accuracy and efficiency of the method

vibration analysis of arbitrarily shaped membranes using non dimensional dynamic influence function abstract in the present study a theoretical formulation based on the collocation method is presented for the vibration analysis of arbitrarily shaped membranes the mathematical relation between the two points of selected collocation points is given by a special function the so called non dimensional dynamic influence function unlike the collocation methods in the literature approximate functions used in this paper are simple one dimensional functions of which the only independent variable is the distance between the two points the function is also a wave type solution that satisfies exactly the given governing differential equation and physically describes the displacement reponse of a point in an infinite membrane due to a unit displacement excited at another point the approximate solution is obtained by linear superposition of non dimensional dynamic influence functions and then boundary conditions are applied at the discrete points the system matrix is always symmetric regardless of the boundary shape of the membrane and the calculated eigenvalues rapidly converge to the exact values thanks to the special function employed in this study moreover the method gives the associated mode shapes successfully without using interpolation functions between the boundary nodes the validity and efficiency of the method proposed in this paper are illustrated through several numerical examples

an integrable sis model we provide a demonstration of the integrability of a classical model of an infectious disease which neither kills nor induces autoimmunity by means of the painleve analysis and use the lie theory of transformation groups to present an explicit solution

numerical verification of solutions for a simplified signorini problem abstract we proposed some numerical methods for the automatic proof of existence of solutions for variational inequalities i e obstacle problems and elastoplastic torsion problems it is based on nakao s method by using finite element approximation and its explicit error estimates for the problem in this paper we present a numerical verification algorithm of exact solutions for a simplified signorini problem in a computer a numerical example for the signorini problem is presented

numerical verification of solutions for some unilateral boundary value problems abstract in this paper we consider a numerical technique which enables us to verify the existence of solutions for some unilateral boundary value problems using the finite element approximations and explicit a priori error estimates we construct in a computer a set of solutions which satisfies the hypothesis of schauder s fixed point theorem for a compact map on a certain sobolev space further the conditions of verifiability by this method are considered and some numerical examples are presented

n dimensional equations with the maximum number of symmetry generators the authors obtain the general class of ordinary differential equations that can be reduced by a point transformation to the free particle equation and given the general form of the lie symmetry generators for these equations they apply these results to obtain the symmetry generators for the n dimensional harmonic oscillator and for a particle in a constant magnetic field

symmetry and singularity properties of second order ordinary differential equations of lie s type iii abstract we extend the work of abraham shrauner b abraham shrauner hidden symmetries and linearization of the modified painleve ince equation j math phys 34 1993 4809 4816 on the linearization of the modified painleve ince equation to a wider class of nonlinear second order ordinary differential equations invariant under the symmetries of time translation and self similarity in the process we demonstrate a remarkable connection with the parameters obtained in the singularity analysis of this class of equations

on the boundary element method for the signorini problem of the laplacian for the laplace equation with signorini boundary conditions two equivalent boundary variational inequality formulations are deduced we investigate the discretization by a boundary element galerkin method and obtain quasi optimal asymptotic error estimates in the underlying sobolev spaces an algorithm based on the decomposition coordination method is used to solve the discretized problems numerical examples confirm the predicted rate of convergence

symmetries of nonlinear differential equations and linearisation a non linear ordinary differential equation is linearisable if it possesses sl 3 r symmetry the conditions under which the abelian two dimensional subalgebras of sl 3 r are sufficient for linearisation are established

explicit h2 estimates and pointwise bounds for solutions of second order elliptic boundary value problems abstract it is well known that the h 2 norm and the c 0 norm of a function u h 2 where r n is a bounded domain n 3 can be estimated in terms of a given uniformly elliptic second order differential operator l and some boundary operator b applied to u if certain regularity assumptions are satisfied if these bounds shall be used for numerical purposes the constants occurring in the estimates must be known explicitly the main goal of the present article is the computation of such explicit constants for simplicity of presentation we restrict ourselves to the case where l u u c x u as an application we prove an existence and inclusion result for nonlinear boundary value problems

second order equation fields and the inverse problem of lagrangian dynamics the transformation properties of determined autonomous systems of second order ordinary differential equations identified as vector fields on the tangent bundle of the space of dependent variables are derived and studied the inverse problem of lagrangian dynamics is studied from this transformation viewpoint as well as the problem of alternative lagrangians in particular regular lagrangians which are analytic as functions of the first derivatives are considered finally the inverse problem for second order systems corresponding to the geodesic flow of a symmetric linear connection is investigated

finite point transformations and linearisation of x f t x the usefulness of finite point transformations is emphasised as a systematic tool for studying the eventual linearisation of ordinary second order differential equations

classification of second order ordinary differential equations admitting lie groups of fibre preserving point symmetries we use elie cartan s method of equivalence to give a complete classification in terms of differential invariants of second order ordinary differential equations admitting lie groups of fibre preserving point symmetries we then apply our results to the determination of all second order equations which are equivalent under fibre preserving transformations to the free particle equation in addition we present those equations of painleve type which admit a transitive symmetry group finally we determine the symmetry group of some equations of physical interest such as the duffing and holmes rand equations which arise as models of non linear oscillators

on the general solution for the modified emden type equation in this paper we demonstrate that the modified equation of emden type mee is integrable either explicitly or by quadrature for any value of and we also prove that the mee possesses appropriate time independent hamiltonian functions for the full range of parameters and in addition we show that the mee is intimately connected with two well known nonlinear models namely the equation of force free duffing type oscillator and the two dimensional lotka volterra equation and thus the complete integrability of the latter two models can also be understood in terms of the mee

projection and self adaptive projection methods for the signorini problem with the bem abstract we propose two new projection methods for solving the signorini problem and study the relationship between them since the signorini boundary condition is equivalent to a projection fixed point problem the methods formulate the signorini boundary condition into a sequence of robin boundary conditions and only require solving a variational problem with simple boundary conditions at each iterative step the convergence speed of the first method depends on the parameter heavily and it is difficult to choose a proper for individual problems to improve the efficiency of the method we propose an adaptive projection method which adjusts the parameter automatically per iteration we establish the convergence analysis of the methods because the signorini boundary condition is given in an iterative form by the potential and its derivative on the boundary of the domain we can easily provide the boundary element approximation of the problem finally we present some numerical simulations which illustrate the performance of the methods

lie algebras associated with scalar second order ordinary differential equations second order ordinary differential equations are classified according to their lie algebra of point symmetries the existence of these symmetries provides a way to solve the equations or to transform them to simpler forms canonical forms of generators for equations with three point symmetries are established it is further shown that an equation cannot have exactly r 4 5 6 7 point symmetries representative s of equivalence class es of equations possessing s 1 2 3 8 point symmetry generator s are then obtained

equivalence classes of second order ordinary differential equations with only a three dimensional lie algebra of point symmetries and linearisation there are seven equivalence classes of second order ordinary differential equations possessing only three lie point symmetries and hence not linearisible by means of a point transformation we examine the representatives of these classes for linearisibility by means of other types of transformation in particular we compare the potential for linearisibility and the possession of the painleve property the complete symmetry group is realised in the standard algebra for each of the equivalence classes

numerical treatment of acoustic problems with boundary singularities by the singular boundary method abstract the singular boundary method sbm is a novel boundary type meshless method based on the fundamental solution of the given governing equation the sbm employs the origin intensity factors to circumvent the singularities resulting from the fundamental solutions in this paper we investigate the acoustic problems with boundary singularities using the sbm this is achieved by combining the sbm with the singularity subtraction techniques where the solution is decomposed into the singular solution and the regular solution the singular solution is derived analytically which satisfies the governing equation and the corresponding boundary conditions containing the singularities then the regular solution is obtained by the sbm numerical examples show the excellent performance of the proposed technique

an efficient wave based method for 2d acoustic problems containing corner singularities abstract the wave based method is an efficient alternative prediction technique based on a trefftz approach which as compared to element based methods can be applied in a wider frequency range at a reasonable cost this paper discusses the use of this method for the particular case of 2d acoustic problems where singularities are present in the corners of the acoustic domain the conventional set of expansion functions used to approximate the dynamic pressure field is extended with special purpose functions that incorporate the singular behaviour in the region around the singular corners this enrichment comes with a beneficial convergence rate while only a small increase of computational effort is incurred this is illustrated for various problem settings including different combinations of both homogeneous and non homogeneous boundary conditions and bounded as well as unbounded problems are considered

a numerical algorithm for the solution of signorini problems in this paper we propose a new iterative algorithm for the solution of a certain class of signorini problems such problems arise in the modelling of a variety of physical phenomena and usually involve the determination of an unknown free boundary here we describe a way of locating the free boundary directly and provide a proof that the algorithm converges when used with analytic methods the advantage of this algorithm is that it can be used in conjunction with any numerical method with minimal development of extra code we demonstrate its application with the boundary element method to some physical problems in both two and three dimensions

analysis of the element free galerkin method for signorini problems abstract an efficient element free galerkin efg method is developed to solve signorini boundary value problems the nonlinear inequality signorini boundary conditions are reduced to a sequence of linear boundary conditions by using a projection iterative scheme then the efg method is used to deduce discrete system equations convergence of the proposed method is discussed numerical examples are finally provided to verify the convergence and high computational accuracy of the method

when nonlinear differential equations are equivalent to linear differential equations a necessary and sufficient condition is established for the existence of a 1 1 transformation of a system of nonlinear differential equations to a system of linear equations the obtained theorems enable one to construct such transformations from the invariance groups of differential equations the hodograph transformation the legendre transformation and lie s transformation of the monge ampsre equation are shown to be special cases noninvertible transformations are also considered examples include burgers equation a nonlinear diffusion equation and the liouville equation introduction in this work we study transformations mapping nonlinear differen tial equations to linear differential equations in a 1 1 manner based upon the group analysis of differential equations we obtain necessary and sufficient conditions for the existence of such transformations the established theorems not only allow us to determine the existence of the transformations but also enable us to actually construct these transformations from invariance groups of the nonlinear equations in the following analysis two types of transformations are considered 1 the invariance groups of differential equations and 2 the mappings which transform nonlinear differential equations to linear differential equations theorems will be proved based upon the following observations clearly if there exists a 1 1 mapping between any two differential equations it must inject properties of one equation into the other including their invariance properties for this reason the often ignored fact that any linear differential equation admits an invariance group related to the superpo sition principle becomes very significant the generator of this particular group depends upon an arbitrary solution of the linear equation it follows then that any nonlinear equation transformable to a linear equation by a 1 1 mappingmust admit an invariance group whose generator depends upon an arbitrary solution of some linear differential equation the idea of comparing invariance groups of differential equations in the search of mappings connecting the equations was first used by bluman in his study of burgers equation 1 and it was applied to the study of the mappings of one dimensional linear parabolic equations to the heat equation 2 in the first section of this paper some basic properties of various transformations are summarized the theorems are presented in the second section the examples in the third section include the hodograph transformation the legendre transformation lie s transformation of themonge ampre equation and the equation ux uxx uyy 0 in the last section we examine properties of noninvertible mappings of burgers equation the diffusion equation u 2ux uy 0 and the liouville equation u y e u respectively into linear equations

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 verification of solutions for variational inequalities in this paper we consider a numerical technique that enables us to verify the existence of solutions for variational inequalities this technique is based on the infinite dimensional fixed point theorems and explicit error estimates for finite element approximations using the finite element approximations and explicit a priori error estimates for obstacle problems we present an effective verification procedure that through numerical computation generates a set which includes the exact solution further a numerical example for an obstacle problem is presented

boundary element free method befm and its application to two dimensional elasticity problems in this study we first discuss the moving least square approximation mls method in some cases the mls may form an ill conditioned system of equations so that the solution cannot be correctly obtained hence in this paper we propose an improved moving least square approximation imls method in the imls method the orthogonal function system with a weight function is used as the basis function the imls has higher computational efficiency and precision than the mls and will not lead to an ill conditioned system of equations combining the boundary integral equation bie method and the imls approximation method a direct meshless bie method the boundary element free method befm for two dimensional elasticity is presented compared to other meshless bie methods befm is a direct numerical method in which the basic unknown quantity is the real solution of the nodal variables and the boundary conditions can be applied easily hence it has higher computational precision for demonstration purpose selected numerical examples are given

a geometric approach to complete reducibility let g be a connected reductive linear algebraic group we use geometric methods to investigate g completely reducible subgroups of g giving new criteria for g complete reducibility we show that a subgroup of g is g completely reducible if and only if it is strongly reductive in g this allows us to use ideas of r w richardson and hilbert mumford kempf from geometric invariant theory we deduce that a normal subgroup of a g completely reducible subgroup of g is again g completely reducible thereby providing an affirmative answer to a question posed by j p serre and conversely we prove that the normalizer of a g completely reducible subgroup of g is again g completely reducible some rationality questions and applications to the spherical building of g are considered many of our results extend to the case of non connected g

the generalized damped cubic equation integrability and general solution the nonlinear ordinary differential equation of the form u f1u f2u f3u3 o representing a generalized damped cubic equation is fully analysed the author finds the general expression for f2 in terms of f1 and f3 that renders the equation integrable also he shows that if f2 satisfies the above mentioned condition the former nonlinear differential equation can always be reduced through adequate changes of variable to the second painleve transcendent

a class of codimension two free boundary problems this review collates a wide variety of free boundary problems which are characterized by the uniform proximity of the free boundary to a prescribed surface such situations can often be approximated by mixed boundary value problems in which the boundary data switches across a codimension two free boundary namely the edge of the region obtained by projecting the free boundary normally onto the prescribed surface as in the parent problem the codimension two free boundary needs to be determined as well as the solution of the relevant field equations but no systematic methodology has yet been proposed for nonlinear problems of this type after presenting some examples to illustrate the surprising behavior that can sometimes occur we discuss the relevance of traditional ideas from the theories of moving boundary problems singular integral equations variational inequalities and stability finally we point out the ways in which further refinement of these techniques is needed if a coherent theory is to emerge

a meshfree numerical method for acoustic wave propagation problems in planar domains with corners and cracks the numerical solution of acoustic wave propagation problems in planar domains with corners and cracks is considered since the exact solution of such problems is singular in the neighborhood of the geometric singularities the standard meshfree methods based on global interpolation by analytic functions show low accuracy in order to circumvent this issue a meshfree modification of the method of fundamental solutions is developed where the approximation basis is enriched by an extra span of corner adapted non smooth shape functions the high accuracy of the new method is illustrated by solving several boundary value problems for the helmholtz equation modelling physical phenomena from the fields of room acoustics and acoustic resonance

the boundary element free method for 2d interior and exterior helmholtz problems abstract the boundary element free method befm is developed in this paper for numerical solutions of 2d interior and exterior helmholtz problems with mixed boundary conditions of dirichlet and neumann types a unified boundary integral equation is established for both interior and exterior problems by using the improved interpolating moving least squares method to form meshless shape functions mixed boundary conditions in the befm can be satisfied directly and easily detailed computational formulas are derived to compute weakly and strongly singular integrals over linear and higher order integration cells three numerical integration procedures are developed for the computation of strongly singular integrals numerical examples involving acoustic scattering and radiation problems are presented to show the accuracy and efficiency of the meshless method

lie group classification of second order ordinary difference equations a group classification of invariant difference models i e difference equations and meshes is presented in the continuous limit the results go over into lie s classification of second order ordinary differential equations the discrete model is a three point one and we show that it can be invariant under lie groups of dimension 0 n 6

short note the method of fundamental solutions for 2d and 3d stokes problems a numerical scheme based on the method of fundamental solutions mfs is proposed for the solution of 2d and 3d stokes equations the fundamental solutions of the stokes equations stokeslets are adopted as the sources to obtain flow field solutions the present method is validated through other numerical schemes for lid driven flows in a square cavity and a cubic cavity test results obtained for a rectangular cavity with wave shaped bottom indicate that the mfs is computationally efficient than the finite element method fem in dealing with irregular shaped domain the paper also discusses the effects of number of source points and their locations on the numerical accuracy

on the stability of the moving least squares approximation and the element free galerkin method in this paper the stability of the moving least squares mls approximation and a stabilized mls approximation is analyzed theoretically and verified numerically it is shown that the stability of the mls approximation deteriorates severely as the nodal spacing decreases while the stability of the stabilized mls approximation is not affected by the nodal spacing the stabilized mls approximation is introduced into the element free galerkin efg method to produce a stabilized efg method theoretical error analysis of the stabilized efg method is provided for boundary value problems with mixed boundary conditions of dirichlet and robin type numerical examples confirm the theoretical results and show that the stabilized efg method has higher computational precision and better stability than the original efg method

numerical verification of solutions for elasto plastic torsion problems abstract in this paper we consider a numerical technique which enables us to verify the existence of solutions for the elasto plastic torsion problems governed by the variational inequality based upon the finite element approximations and the explicit a priori error estimates for a simple problem we present an effective verification procedure that through numerical computation generates a set which includes the exact solution this paper is an extension of the previous paper 1 in which we mainly dealt with the obstacle problems but some special techniques are utilized to verify the solutions for nondifferentiable nonlinear equations concerned with the present problem a numerical example is illustrated

on the lie symmetries of the classical kepler problem the standard version of noether s theorem when applied to the classical kepler problem leads to the constants of energy and angular momentum but does not give the hidden symmetry known as the runge lenz vector lie s theory of differential equations is used to obtain all three constants of motion the transformations of solutions under the point transformations to which these constants correspond are studied the results are generalised to n dimensions

invertible point transformations painleve analysis and anharmonic oscillators the techniques of an invertible point transformation and the painleve analysis can be used to construct integrable ordinary differential equations the authors compare both techniques for anharmonic oscillators

infinitesimal symmetry transformations ii some one dimensional nonlinear systems the converse problem of similarity analysis is discussed for the infinitesimal symmetry transformations of ordinary second order differential equations which are nonlinear in x and may be linear or nonlinear in x a natural classification of the problem arises according to the highest order n of nonlinearity in x the completely general maximal lie algebra is obtained for the case n 3 in the case n 4 one has besides the system of differential equations for the infinitesimal generators an extra set of anholonomic constraints which operates as a symmetry breaking mechanism producing a strong reduction in the number of surviving parameters miscellaneous examples are given which illustrate some features of similarity analysis of nonlinear systems the infinitesimal point transformation symmetries of the van der pol oscillator are also briefly discussed

contact symmetry algebras of scalar second order ordinary differential equations there is a natural link between contact symmetries symmetries that leave invariant the first order contact form and first integrals of a given second order ordinary differential equation it will be shown that the contact symmetry algebra of a general second order ordinary differential equation is infinite dimensional and it is generated by the functionally independent first integrals of the equation moreover the contact symmetry algebras of second order equations admitting one two three and eight point symmetries are obtained

linearization of second order ordinary differential equations via cartan s equivalence method abstract we use cartan s equivalence method to study the differential invariants of a single second order ordinary differential equation relative to the pseudo group of point transformations as a result of the analysis a simple characterization is given of those second order equations which are linearizable by a point transformation

singular boundary method for heat conduction problems with certain spatially varying conductivity the singular boundary method sbm is a recent boundary type meshless collocation method in which the solution of a given problem is expanded as a linear combination of the fundamental solutions in terms of the source points the method circumvents the fictitious boundary long perplexing the method of fundamental solution mfs by the introduction of the concept of origin intensity factors oifs this paper documents the first attempt to extend the method to heat conduction problems in nonhomogeneous materials we derive the fundamental solutions of heat conduction problems with the thermal conductivity of the quadratic exponential and trigonometric material variations in three directions furthermore we firstly theoretically derive the value of the oif for the natural logarithm function which is later extended to the oifs for a group of fundamental solutions the feasibility accuracy and stability of the presented sbm formulation are confirmed for both two 2d and three dimensional 3d examples

lagrangian formalism for nonlinear second order riccati systems one dimensional integrability and two dimensional superintegrability the existence of a lagrangian description for the second order riccati equation is analyzed and the results are applied to the study of two different nonlinear systems both related with the generalized riccati equation the lagrangians are non natural and the forces are not derivable from a potential the constant value e of a preserved energy function can be used as an appropriate parameter for characterizing the behavior of the solutions of these two systems in the second part the existence of two dimensional versions endowed with superintegrability is proved the explicit expressions of the additional integrals are obtained in both cases finally it is proved that the orbits of the second system that represents a nonlinear oscillator can be considered as nonlinear lissajous figures

symmetry lie algebras of nth order ordinary differential equations abstract we show that an nth n 3 order linear ordinary differential equation has exactly one of n 1 n 2 or n 4 the maximum point symmetries the lie algebras corresponding to the respective numbers of point symmetries are obtained then it is shown that a necessary and sufficient conditon for an nth n 3 order equation to be linearizable via a point transformation is that it must admit the n dimensional abelian algebra na1 a1 a1 a1 we discuss in detail the symmetry realizations of n 1 a1 s a1 finally we prove that an nth n 3 order equation q n h t q qn 1 cannot admit exactly an n 3 dimensional algebra of point symmetries which is a subalgebra of na1 gl 2 r

hidden symmetries and linearization of the modified painleve ince equation the linearization and hidden symmetries of the modified painleve ince equation y yy y3 0 where and are constants are presented the linearization of this equation by a nonlocal transformation yields a damped stable or growing unstable harmonic oscillator equation for 0 hidden symmetries are analyzed by transforming the modified painleve ince equation to a third order ordinary differential equation ode which in general is invariant under a three parameter group by a riccati transformation a type i hidden symmetry is found of a second order ode found from the third order ode where a symmetry is lost in the reduction of order by the non normal subgroup invariants a type ii hidden symmetry occurs in the third order ode because the symmetries of a second order ode reduced from the third order ode by another set of normal subgroup invariants are increased

numerical verification of solutions for signorini problems using newton like method we proposed a numerical method to verify the existence of solutions for a simplified signorini problem comput math appl 2000 40 1003 1013 using sequential iteration method we numerically constructed a set containing solutions that satisfies the hypothesis of schauder s fixed point theorem in a certain sobolev space it is difficult to apply this method to the problem of which associated operator is not retractive in a neighborhood of the solution in this paper in order to overcome such a difficulty we describe an alternative approach to this problem numerical examples are presented copyright 2007 john wiley sons ltd

a meshless integration free and boundary only rbf technique based on the radial basis function rbf nonsingular general solution and dual reciprocity method drm this paper presents an inherently meshless integration free boundary only rbf collocation technique for numerical solution of various partial differential equation systems the basic ideas behind this methodology are very mathematically simple in this study the rbfs are employed to approximate the inhomogeneous terms via the drm while nonsingular general solution leads to a boundary only rbf formulation for homogenous solution the present scheme is named as the boundary knot method bkm to differentiate it from the other numerical techniques in particular due to the use of nonsingular general solutions rather than singular fundamental solutions the bkm is different from the method of fundamental solution in that the former does not require the artificial boundary and results in the symmetric system equations under certain conditions the efficiency and utility of this new technique are validated through a number of typical numerical examples completeness concern of the bkm due to the sole use of the nonsingular part of complete fundamental solution is also discussed

singular boundary method for solving plane strain elastostatic problems this study documents the first attempt to apply the singular boundary method sbm a novel boundary only collocation method to two dimensional 2d elasticity problems unlike the method of fundamental solutions mfs the source points coincide with the collocation points on the physical boundary by using an inverse interpolation technique to regularize the singularity of the fundamental solution of the equation governing the problems of interest three benchmark elasticity problems are tested to demonstrate the feasibility and accuracy of the proposed method through detailed comparisons with the mfs boundary element method bem and finite element method fem

a galerkin boundary node method and its convergence analysis the boundary node method bnm exploits the dimensionality of the boundary integral equation bie and the meshless attribute of the moving least square mls approximations however since mls shape functions lack the property of a delta function it is difficult to exactly satisfy boundary conditions in bnm besides the system matrices of bnm are non symmetric a galerkin boundary node method gbnm is proposed in this paper for solving boundary value problems in this approach an equivalent variational form of a bie is used for representing the governing equation and the trial and test functions of the variational formulation are generated by the mls approximation as a result boundary conditions can be implemented accurately and the system matrices are symmetric total details of numerical implementation and error analysis are given for a general bie taking the dirichlet problem of laplace equation as an example we set up a framework for error estimates of gbnm some numerical examples are also given to demonstrate the efficacity of the method

properties of second order ordinary differential equations invariant under time translation and self similar transformation the general form of a second order ordinary differential equation invariant under time translation and self similarity is obtained together with its solution in parametric form next two representatives of two different families of such equations are studied in terms of rescaled phase space variables the first example has a simple physical interpretation and its limit cycle properties and period are easily derived similar results are found for the second example but the physical interpretation is less obvious the invariant equations are used as a basis to study the asymptotic behavior of related noninvariant equations thereby underlining the critical value nature of the parameters for which a self similar solution sss exists

a numerical verification method for the existence of weak solutions for nonlinear boundary value problems abstract in this paper we consider a numerical technique which enables us to verify the existence of solutions for nonlinear two point boundary value problems bvp we formulate the problem as a fixed point of a newton like operator and present a verification algorithm by computer based on sadovskii s fixed point theorem in order to compute the newton type iterative sequences in infinite dimensional space two concepts the rounding and the rounding error are introduced also some numerical examples are illustrated we emphasize that since the present method uses the weak formulation of bvp and the finite element approximations instead of the existing validation techniques it is aslo applicable in principle to the bvp for partial differential equations as it stands

generalized lie symmetries and complete integrability of certain nonlinear hamiltonian systems with three degrees of freedom a systematic method for investigating the existence of nontrivial generalized lie symmetries is presented and the associated integrals of motion for nonlinear oscillator systems with three degrees of freedom defined in terms of the lagrangian by l 1 2 x2 y2 z2 v x y z are constructed then the method is applied to study the integrability properties of quartically and cubically coupled nonlinear oscillators with three degrees of freedom compatibility with the painleve property is also investigated

meshless projection iterative analysis of signorini problems using a boundary element free method this paper presents a meshless method based on coupling a boundary element free method befm with a new projection iterative scheme for signorini problems using the new iterative scheme the nonlinear complementary signorini boundary conditions are transformed into neumann boundary conditions then mixed elliptic problems are formed and are solved by the befm in this method only a nodal data structure on the boundary is required and the coefficient matrices of the discrete system equations only have to be computed once in the whole iterative process convergence of the iterative scheme is discussed theoretically numerical examples involving beach percolation and an electropaint process are given to illustrate the convergence rate and high computational efficiency of the method

first integrals for the modified emden equation q α t q qn 0 it is shown that the modified emden equation q t q qn 0 possesses first integrals for functions t other than kt 1 the function t is obtained explicitly in the case n 3 and parametrically for other n 2 the case n 2 is seen to be particularly difficult to solve