The Time-Marching Method of Fundamental Solutions for Multi-Dimensional Telegraph Equations

Abstract

The telegraph equations are solved by using the meshless numerical method called the time-marching method of fundamental solutions (TMMFS) in this paper. The present method is based on the method of fundamental solutions, the method of particular solutions and the Houbolt finite difference scheme. The TMMFS is a meshless numerical method, and has the advantages of no mesh building and numerical quadrature. Therefore in this study we eventually solved the multi-dimensional telegraph equation problems in irregular domain. There are totally six numerical examples demonstrated, in order they are one-dimensional telegraph equation, one-dimensional non-decaying telegraph problem, two-dimensional telegraph equation in irregular domain, three-dimensional telegraph problem in cubic domain, three-dimensional telegraph equation in irregular domain and three-dimensional fixed boundary telegraph problem in irregular domain. All numerical results have shown good efficiency and accuracy of the algorithm, thus demonstrated the present meshless numerical method of the TMMFS is applicable for further applications in solving the multi-dimensional telegraph equation in irregular domain.