Homotopy analysis and homotopy Padé methods for (1+1) and (2+1)‐dimensional dispersive long wave equations

Abstract

Purpose

The purpose of this paper is to obtain analytic solutions of the (1+1) and (2+1)‐dimensional dispersive long wave equations by the homotopy analysis and the homotopy Padé methods.

Design/methodology/approach

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.

Findings

The approximation solutions by [m,m] homotopy Padé technique is often independent of auxiliary parameter ℏ and this technique accelerates the convergence of the related series.

Originality/value

In this paper, analytic solutions of the (1+1) and (2+1)‐dimensional dispersive long wave equations are obtained by the homotopy analysis and the homotopy Padé methods. 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 ℏ and this technique accelerates the convergence of the related series.

Citation

Jabbari, A., Kheiri, H. and Yildirim, A. (2013), "Homotopy analysis and homotopy Padé methods for (1+1) and (2+1)‐dimensional dispersive long wave equations", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 23 No. 4, pp. 692-706. https://doi.org/10.1108/09615531311323818