Eur. Phys. J. Plus (2017) 132: 263
https://doi.org/10.1140/epjp/i2017-11529-2

Regular Article

A meshless technique based on the pseudospectral radial basis functions method for solving the two-dimensional hyperbolic telegraph equation

Department of Mathematics, Imam Khomeini International University, 34149, Ghazvin, Iran

^* e-mail: emam_me@yahoo.com

Received: 8 March 2017
Accepted: 4 May 2017
Published online: 13 June 2017

Abstract

In this paper, the pseudospectral radial basis functions method is proposed for solving the second-order two-space-dimensional telegraph equation in regular and irregular domain. The proposed numerical method, which is truly meshless, is based on a time stepping procedure to deal with the temporal part of the solution combined with radial basis function differentiation matrices for discretizing the spatial derivatives. Here, we extended the pseudospectral radial basis functions method for two-dimensional hyperbolic telegraph equations in irregular domain. A cross-validation technique is used to optimize the shape parameter for the basis functions. Numerical results and comparisons are given to validate the presented method for solving the two-dimensional telegraph equation on both regular and irregular domains which show that the approximate solutions are in good agreement with the exact solution. The obtained results showed that the proposed method is easy to apply for multidimensional problems and equally applicable to both the regular and irregular domains.