An accurate meshless collocation technique for solving two-dimensional hyperbolic telegraph equations in arbitrary domains

Abstract

The paper presents an accurate meshless collocation method to solve time-dependent hyperbolic telegraph equations in arbitrary domains. The discretization of temporal variables is achieved by the Crank-Nicolson finite difference scheme. The solution to the discretized system is approximated by a primary approximation and corrected radial basis functions with unknown parameters. The primary approximation is obtained by matching the proposed boundary conditions. Each of the corrected radial basis function is the sum of a radial basis function and a specific correcting function obtained from the governing equations. The unknown weight parameters are obtained by collocating the approximation with the governing equations. Several numerical experiments are considered to verify the efficacy of the proposed method.