Moving Least Squares (MLS) Method for the Nonlinear Hyperbolic Telegraph Equation with Variable Coefficients

Abstract

Telegraph equation which widely used for modeling many engineering and physical phenomena has considered by some researchers in recent years. In this paper, a numerical scheme based on the moving least squares (MLS) approximation and finite difference method (FDM) is proposed for solving a class of the nonlinear hyperbolic telegraph equation with variable coefficients. In the new developed scheme, we use collocation points and approximate solution of the problem under study by using MLS approximation. The MLS method is a meshless approach and does not need any background mesh structure. A time stepping approach is employed for the first- and second-order time derivatives. The proposed method provides a semi-discrete solutions for the problems under study. In space domain, the MLS approximation and in time domain, the finite difference technique are employed. This method after discretization leads to a linear system of algebraic equations. Some numerical results are given and compared with analytical solutions to demonstrate the validity and efficiency of the proposed technique.