meshfree approximation methods with matlab

As one kind of mesh method, finite difference methods are adopted to solve this partial differential equations. Over the past several decades, many numerical methods have been developed to solve boundary-value problems involving ordinary and partial differential equations, such as the finite difference, finite elements, and multigrid methods. It arises in fields like acoustics, electromagnetics, and fluid dynamics. The wave equation is also an important second-order linear partial differential equation for the description of waves, such as sound waves, light waves, and water waves.

Telegraph equations describe various phenomena in many applied fields, such as a planar random motion of a particle in fluid flow, transmission of electrical impulses in the axons of nerve and muscle cells, propagation of electromagnetic waves in superconducting media, and propagation of pressure waves occurring in pulsatile blood flow in arteries. The cases and correspond to the telegraph problem and wave problem, respectively. Where, , are constants, and are given analytic functions, and. This paper is devoted to the numerical computation of the nonhomogeneous time-dependent problem with the following form:

The results of numerical experiments are presented and are compared with analytical solutions to confirm the accuracy of our scheme.

Finite difference method is adopted to deal with time variable and its derivative, and radial basis functions method is developed for spatial discretization. We propose a new numerical meshfree scheme to solve time-dependent problems with variable coefficient governed by telegraph and wave equations which are more suitable than ordinary diffusion equations in modelling reaction diffusion for such branches of sciences.

Meshfree approximation methods with matlab