Homotopy Padé method for solving second-order one-dimensional telegraph equation

Abstract

Purpose

The purpose of this paper is to obtain analytic solutions of telegraph equation by the homotopy Padé method.

Design/methodology/approach

The authors used Maple Package to calculate the solutions obtained from the homotopy Padé method.

Findings

The obtained approximation by using homotopy method contains an auxiliary parameter which is a simple way to control and adjust the convergence region and rate of solution series. The approximation solutions by [m, m] homotopy Padé technique are often independent of auxiliary parameter h and this technique accelerates the convergence of the related series. Finally, numerical results for some test problems with known solutions are presented and the numerical results are given to show the efficiency of the proposed techniques.

Originality/value

The paper is shown that homotopy Padé technique is a promising tool with accelerated convergence for complicated nonlinear differential equations.

Citation

Jabbari, A., Kheiri, H. and Yildirim, A. (2013), "Homotopy Padé method for solving second-order one-dimensional telegraph equation", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 23 No. 7, pp. 1192-1203. https://doi.org/10.1108/HFF-09-2011-0192