THE METHOD OF FUNDEMENTAL SOLUTIONS FOR THE MULTI-DIMENSIONAL WAVE EQUATIONS

Abstract

In this paper, a meshless method is developed for solving multi-dimensional wave equations. The proposed method is based on the method of particular solution (MPS), the method of fundamental solutions (MFS) and the Houbolt finite difference (FD) method. The wave equation is considered as a Poisson-type equation with the time-dependent source term. The Houbolt method is applied to avoid the difficult problems for dealing with the initial conditions in forming the linear algebra system. The works of space discretization are dependent on the method of particular solution and the method of fundamental solutions. There are three numerical examples considered in this paper, such as the string vibration and wave vibration problems. Numerical validations have proven that the proposed method is a highly efficient and accurate meshless numerical tool for solving wave equations in engineering and sciences by comparing with analytical solution and other numerical solutions.