A numerical method for solving the hyperbolic telegraph equation

Abstract

Recently, it is found that telegraph equation is more suitable than ordinary diffusion equation in modelling reaction diffusion for such branches of sciences. In this article, we propose a numerical scheme to solve the one-dimensional hyperbolic telegraph equation using collocation points and approximating the solution using thin plate splines radial basis function. The scheme works in a similar fashion as finite difference methods. The results of numerical experiments are presented, and are compared with analytical solutions to confirm the good accuracy of the presented scheme.

Laplace Transform Collocation Method for Solving Hyperbolic Telegraph Equation

“…Recently, telegraph equation is found to be more suitable than ordinary diffusion equation in modelling reaction diffusion for such branches of science [5]. Without any doubt, (1) and its solution are of great importance in many areas of application.…”

A Numerical Study of One-Dimensional Hyperbolic Telegraph Equation

“…In [2], a numerical scheme for solving the secondorder one-space-dimensional linear hyperbolic equation has been presented by using the shifted Chebyshev cardinal functions. Dehghan and Shokri [3,4] have studied a numerical scheme to solve one and two-dimensional hyperbolic equations using collocation points and the thin-plate-spline radial basis functions. In [34], a numerical method, based on the combination of a high-order compact finite-difference scheme was used to approximate the spatial derivative and the collocation technique for the time component was proposed to solve the one-space-dimensional linear hyperbolic equation.…”

A Collocation Method for Numerical Solution of Hyperbolic Telegraph Equation with Neumann Boundary Conditions

“…El-Azab and El-Ghamel [1] have used Routhe-wavelet method for the numerical solution of telegraph equation. Dehghan and Shokri [2] presented a meshless method based on collocation with radial basis functions. Spline solutions of hyperbolic telegraph equation have been studied in [3][4][5][6].…”