The Method of Particular Solutions (MPS) for Solving One-Dimensional Hyperbolic Telegraph Equation

Abstract

In this paper, the method of particular solution (MPS) is employed for the numerical solution of the one-dimensional (1D) telegraph equation based on radical basis functions (RBFs). Coupled with the time discretization and MPS, the proposed method is a truly meshless method which requires neither domain or boundary discretization. The algorithm is very simple so it is very easy to implement. The results of numerical experiments are presented, and are compared with analytical solutions to confirm the good accuracy of the presented scheme, the obtained numerical results also have been compared with the results obtained by some existing methods to verify the accurate nature of our method.