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

Abstract

PurposeThe 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/approachThe 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.FindingsThe 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/valueIn 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.

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