absolute value equations abstract we investigate existence and nonexistence of solutions for np hard equations involving absolute values of variables ax x b where a is an arbitrary n n real matrix by utilizing an equivalence relation to the linear complementarity problem lcp we give existence results for this class of absolute value equations aves as well as a method of solution for special cases we also give nonexistence results for our ave using theorems of the alternative and other arguments

a meshless local collocation method for time fractional diffusion wave equation abstract in this manuscript we present a radial basis function based local collocation method for solving time fractional diffusion wave equation the advantage of the local collocation method is only the discretization points located in each sub domain surrounding the collocation point need to be considered it also avoids the ill conditioning problem arises due to the use of global collocation method the theoretical stability and convergence of the proposed time semi discrete scheme are also discussed numerical experiments for one dimension and two dimension problems are carried out it is shown that the present method is efficient and numerical results have nice agreements with theoretical result

continuous extension of the geometric control method in this paper we give a continuous version valid for flows of the geometric control method introduced by toroczkai et al 1994 and constructed for mappings on 2d poincare sections this method does not require explicit knowledge of the dynamics just a rough location of the periodic orbit and a single parameter easily computed from four data points applicability in numerical and real experiments is discussed

a numerical study of some radial basis function based solution methods for elliptic pdes abstract during the last decade three main variations have been proposed for solving elliptic pdes by means of collocation with radial basis functions rbfs in this study we have implemented them for infinitely smooth rbfs and then compared them across the full range of values for the shape parameter of the rbfs this was made possible by a recently discovered numerical procedure that bypasses the ill conditioning which has previously limited the range that could be used for this parameter we find that the best values for it often fall outside the range that was previously available we have also looked at piecewise smooth versus infinitely smooth rbfs and found that for pde applications with smooth solutions the infinitely smooth rbfs are preferable mainly because they lead to higher accuracy in a comparison of rbf based methods against two standard techniques a second order finite difference method and a pseudospectral method the former gave a much superior accuracy

p sv wave propagation in heterogeneous media velocity stress finite difference method i present a finite difference method for modeling p sv wave propagation in heterogeneous media this is an extension of the method i previously proposed for modeling sh wave propagation by using velocity and stress in a discrete grid the two components of the velocity cannot be defined at the same node for a complete staggered grid the stability condition and the p wave phase velocity dispersion curve do not depend on the poisson s ratio while the s wave phase velocity dispersion curve behavior is rather insensitive to the poisson s ratio therefore the same code used for elastic media can be used for liquid media where s wave velocity goes to zero and no special treatment is needed for a liquid solid interface typical physical phenomena arising with p sv modeling such as surface waves are in agreement with analytical results the weathered layer and corner edge models show in seismograms the same converted phases obtained by previous authors this method gives stable results for step discontinuities as shown for a liquid layer above an elastic half space the head wave preserves the correct amplitude finally the corner edge model illustrates a more complex geometry for the liquid solid interface as the poisson s ratio v increases from 0 25 to 0 5 the shear converted phases are removed from seismograms and from the time section of the wave field

seismic modeling with radial basis function generated finite differences abstractseismic exploration is the primary tool for finding and mapping out hydrocarbon deposits we have considered the 2d forward modeling problem the subsurface structures were assumed to be known and the task was to simulate elastic wave propagation throughout the medium many traditional approaches to solving this problem account for material interfaces by allowing model parameter values such as wave speed and density to vary either sharply or smoothly between adjacent data points although simple to implement these strategies typically produce solutions that feature a suboptimal first order convergence to the true solution spatial discretization based on radial basis function generated finite differences rbf fds has previously been shown to offer high accuracy and algebraic simplicity when using scattered layouts of computational nodes we have now developed this method further to provide third order accuracy not only throughout smooth regions but also for wave reflections and transmission

brief converting chaos into periodic motion by state feedback control a simple control method is presented to convert chaos into periodic motion by using linear state feedback of an available system variable the low periodic orbits can be derived from the chaotic attractor with slight change of the dynamical structure in the original dynamics melnikov s perturbation method in generalized hamiltonian systems is introduced to explain the control mechanism of directing chaotic motion towards low periodic motion in the lorenz equations moreover the existence of periodic orbits is examined in the perturbed lorenz system simulation results verify the effectiveness of melnikov s analysis

fractal boundaries in open hydrodynamical flows signatures of chaotic saddles we introduce the concept of fractal boundaries in open hydrodynamical flows based on two gedanken experiments carried out with passive tracer particles colored differently it is shown that the signature for the presence of a chaotic saddle in the advection dynamics is a fractal boundary between regions of different colors the fractal parts of the boundaries found in the two experiments contain either the stable or the unstable manifold of this chaotic set we point out that these boundaries coincide with streak lines passing through appropriately chosen points as an illustrative numerical experiment we consider a model of the von k arm an vortex street a time periodic two dimensional flow of a viscous fluid around a cylinder

conserved quantities of some hamiltonian wave equations after full discretization hamiltonian pdes have some invariant quantities which would be good to conserve with the numerical integration in this paper we concentrate on the nonlinear wave and schrodinger equations under hypotheses of regularity and periodicity we study how a symmetric space discretization makes that the space discretized system also has some invariants or nearly invariants which well approximate the continuous ones we conjecture some facts which would explain the good numerical approximation of them after time integration when using symplectic runge kutta methods or symmetric linear multistep methods for second order systems

controlling complexity using forcing simulations and experiments we report the successful manipulation of non linear dynamics using external forcing in the case of temporal systems a model system involving ordinary differential equations ode s was used for simulations experiments were carried out in a single anode electrochemical cell numerical and experimental results indicate that under the influence of external forcing control of complexity and a change in periodicity of the autonomous dynamics can be achieved a natural extension of this work involves analyzing the effects of global and local forcing on complex spatio temporal behavior a numerical model involving partial differential equations pde s was used for simulating the dynamics of this extended system an electrochemical cell involving multiple anodes was used for the corresponding experiments in simulations and in experiments suppression of spatio temporal complexity is observed for the two forcing global and local methods

approximation to the k th derivatives by multiquadric quasi interpolation method quasi interpolation is very useful in the study of approximation theory and its applications since it can yield solutions directly without the need to solve any linear system of equations based on the good performance simple to evaluate of multiquadric functions the advantages approximation order convexity and monotonlcity preserving of multiquadric quasi interpolation have been widely discussed however it is usually only for the approximation properties of the function itself and the good properties for derivatives whereas the high order derivatives have been largely ignored in this paper we go further into the approximation properties to the k th derivatives by using multiquadric quasi interpolation furthermore we develop two kinds of multiquadric quasi interpolation schemes on bounded interval x 0 x n whose derivatives converge to the corresponding derivatives of the approximated functions finally the numerical experiments are presented to confirm the accuracy of the presented scheme both theoretical results and numerical examples show this scheme provides good accuracy even if the data points in x 0 x n are irregularly distributed

fourth order finite difference p sv seismograms i describe the properties of a fourth order accurate space second order accurate time two dimensional p sk finite difference scheme based on the madariagavirieux staggered grid formulation the numerical scheme is developed from the first order system of hyperbolic elastic equations of motion and constitutive laws expressed in particle velocities and stresses the madariaga virieux staggered grid scheme has the desirable quality that it can correctly model any variation in material properties including both large and small poisson s ratio materials with minimal numerical dispersion and numerical anisotropy dispersion analysis indicates that the shortest wavelengths in the model need to be sampled at 5 gridpoints wavelength the scheme can be used to accurately simulate wave propagation in mixed acoustic elastic media making it ideal for modeling marine problems explicitly calculating both velocities and stresses makes it relatively simple to initiate a source at the free surface or within a layer and to satisfy free surface boundary conditions benchmark comparisons of finite difference and analytical solutions to lamb s problem are almost identical as are comparisons of finite difference and reflectivity solutions for elastic elastic and acoustic elastic layered models

numerical methods for hamiltonian pdes the paper provides an introduction and survey of conservative discretization methods for hamiltonian partial differential equations the emphasis is on variational symplectic and multi symplectic methods the derivation of methods as well as some of their fundamental geometric properties are discussed basic principles are illustrated by means of examples from wave and fluid dynamics

an efficient method for optimal correcting of absolute value equations by minimal changes in the right hand side our goal in this work is to give an optimum correction of the infeasible absolute value equations ave in order to make the mentioned system feasible we apply the minimal correction using the l 2 norm by changing just the right hand vector we will show that this problem can be formulated as an unconstrained optimization problem with a quadratic objective function we propose an extension of newton s method for solving unconstrained objective optimization some examples are provided to illustrate the efficiency and validity of our proposed method

symplectic wavelet collocation method for hamiltonian wave equations this paper introduces a novel symplectic wavelet collocation method for solving nonlinear hamiltonian wave equations based on the autocorrelation functions of daubechies compactly supported scaling functions collocation method is conducted for the spatial discretization which leads to a finite dimensional hamiltonian system then appropriate symplectic scheme is employed for the integration of the hamiltonian system under the hypothesis of periodicity the properties of the resulted space differentiation matrix are analyzed in detail conservation of energy and momentum is also investigated various numerical experiments show the effectiveness of the proposed method

seismic modeling with radial basis function generated finite differences rbf fd a simplified treatment of interfaces abstract in a previous study of seismic modeling with radial basis function generated finite differences rbf fd we outlined a numerical method for solving 2 d wave equations in domains with material interfaces between different regions the method was applicable on a mesh free set of data nodes it included all information about interfaces within the weights of the stencils allowing the use of traditional time integrators and was shown to solve problems of the 2 d elastic wave equation to 3rd order accuracy in the present paper we discuss a refinement of that method that makes it simpler to implement it can also improve accuracy for the case of smoothly variable model parameter values near interfaces we give several test cases that demonstrate the method solving 2 d elastic wave equation problems to 4th order accuracy even in the presence of smoothly curved interfaces with jump discontinuities in the model parameters

a high order modified levenberg marquardt method for systems of nonlinear equations with fourth order convergence fan 2014 presented an accelerated modified levenberg marquardt method for nonlinear equations at every iteration the accelerated modified lm method computed not only a lm trial step but also an additional approximate lm step which employed a line search in this paper based on the accelerated modified lm method we compute the approximate lm step one more time at every iteration and obtain a high order accelerating modified levenberg marquardt method under the local error bound condition which is weaker than nonsingularity the convergence order of this new method is shown to be fourth a globally convergence is also given by the trust region technique numerical results show that the new method is efficient and could save many calculations of the jacobian

control of nmr laser chaos in high dimensional embedding space the unstable periodic orbits of a chaotic nmr laser have been identified and classified according to their stability properties the dynamical control method by ott grebogi and yorke ogy phys rev lett 64 1196 1990 has been successfully applied in a six dimensional embedding space as required for a proper reconstruction of the attractors an improved method has then been implemented in order to circumvent the occurrence of several possibly complex unstable eigenvalues in the standard ogy procedure and has shown superior performance finally an extension to several control stations per poincar e time is discussed

a gfdm with pml for seismic wave equations in heterogeneous media abstract the interior of the earth is heterogeneous with different materials and may have complex geometry the free surface can also be uneven therefore the use of a meshless method with the possibility of using an irregular grid point distribution can be of interest for modelling this kind of problem this paper shows the application of gfdm to the problem of seismic wave propagation in 2 d to use this method in unbounded domains one must truncate the computational grid point avoiding reflection from the edges pml absorbing boundary condition has then been included in the numerical model proposed in this work

controlling transient chaos the method of ott grebogi and yorke 1990 is extended to control transient chaos the controlled signal then exhibits a periodic behaviour which is qualitatively different from that of the actual attractor the time needed to achieve control is shown to be constant and to lie in the order of magnitude of the transient lifetime the number of controlled trajectories however decreases the maximum perturbation according to a power law applicability to experimental situations and comparison with permanent chaotic cases are discussed

poincare maps of duffing type oscillators and their reduction to circle maps ii methods and numerical results bifurcation diagrams and plots of lyapunov exponents in the r plane for duffing type oscillators exhibit a regular pattern of repeating self similar tongues with complex internal structure we demonstrate here how this behaviour is easily understood qualitatively and quantitatively from a poincare map of the system in action angle variables in the limit of large driving force or equivalently small driving frequency this map approaches the one dimensional form as derived in paper i this second paper describes our approach to calculating the various constants and functions introduced in paper i it gives numerical applications of the theory and tests its range of validity by comparison with results from the numerical integration of duffing type equations finally we show how to extend the range in the parameter space where the map is applicable

levenberg marquardt method for solving systems of absolute value equations in this paper we suggest and analyze the levenberg marquardt method for solving system of absolute value equations a x x b where a r n i n b r n and x r n are unknown we present different line search methods to convey the main idea and the significant modifications we discuss the convergence of the proposed method we consider numerical examples to illustrate the implementation and efficiency of the method results are very encouraging and may stimulate further research in this direction

controlling chaotic dynamical systems abstract we describe a method that converts the motion on a chaotic attractor to a desired attracting time periodic motion by making only small time dependent perturbations of a control parameter the time periodic motion results from the stabilization of one of the infinite number of previously unstable periodic orbits embedded in the attractor the present paper extends that of ott grebogi and yorke phys rev lett 64 1990 1196 allowing for a more general choice of the feedback matrix and implementation to higher dimensional systems the method is illustrated by an application to the control of a periodically impulsively kicked dissipative mechanical system with two degrees of freedom resulting in a four dimensional map the double rotor map a key issue addressed is that of the dependence of the average time to achieve control on the size of the perturbations and on the choice of the feedback matrix

periodic orbits as the skeleton classical and quantum chaos a description of a low dimensional deterministic chaotic system in terms of unstable periodic orbits cycles is a powerful tool for theoretical and experimental analysis of both classical and quantum deterministic chaos comparable to the familiar perturbation expansions for nearly integrable systems the infinity of orbits characteristic of a chaotic dynamical system can be resummed and brought to a selberg product form dominated by the short cycles and the eigenvalue spectrum of operators associated with the dynamical flow can then be evaluated in terms of unstable periodic orbits methods for implementing this computation for finite subshift dynamics are introduced

symplectic integration of hamiltonian wave equations the numerical integration of a wide class of hamiltonian partial differential equations by standard symplectic schemes is discussed with a consistent hamiltonian approach we discretize the hamiltonian and the poisson structure separately then form the the resulting ode s the stability accuracy and dispersion of different explicit splitting methods are analyzed and we give the circumstances under which the best results can be obtained in particular when the hamiltonian can be split into linear and nonlinear terms many different treatments and examples are compared

sympletic finite difference approximations of the nonlinear klein gordon equation we analyze three finite difference approximations of the nonlinear klein gordon equation and show that they are directly related to symplectic mappings two of the schemes the perring skyrme and ablowitz kruskal ladik are long established and the third is a new higher order accurate scheme we test the schemes on traveling wave and periodic breather problems over long time intervals and compare their accuracy and computational costs with those of symplectic and nonsymplectic method of lines approximations and a nonsymplectic energy conserving method

controlling hamiltonian chaos the method for stabilizing an unstable periodic orbit in chaotic dynamical systems originally formulated by ott grebogi and yorke ogy is not directly applicable to chaotic hamiltonian systems the reason is that an unstable periodic orbit in such systems often exhibits complex conjugate eigenvalues at one or more of its orbit points in this paper we extend the ogy stabilization method to control hamiltonian chaos by incorporating the notion of stable and unstable directions at each periodic point we also present an algorithm to calculate the stable and unstable directions other issues specific to the control of hamiltonian chaos are also discussed

a symplectic procedure for two dimensional coupled elastic wave equations using radial basis functions interpolation abstract this study proposes a meshless symplectic algorithm for two dimensional coupled elastic waves which satisfy the equations of linear isotropic elasticity on a rectangular domain with appropriate initial and boundary conditions this method is based on a combination of radial basis functions rbfs collocation and geometric integrators the method involves two steps first the spatial discretization by using rbfs interpolation transforms the seismic waves into a finite dimensional hamiltonian system then evolves the semi discretized system by using symplectic integrators furthermore the conservations of energy and symplectic structure are investigated the truncation error and global error of the method are estimated numerical experiments show that the scheme is efficient easy to implement with the scattered knots and possesses a good behavior in the long time integration