Solution of the two-dimensional telegraph equation via the local radial basis functions method

Abstract

In the present study, we utilize the local meshless method for solving second order hyperbolic partial differential equation in two dimensions. First we apply the Crank-Nicolson difference scheme for the time derivative and the local radial basis functions (LRBFs) collocation method for the spatial derivative. The local approach breaks down the problem domain into subdomains and results small matrix system for each data. Some numerical examples are included to verify the computational efficiency of the proposed method.