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Article
Publication date: 20 September 2011

Syed Tauseef Mohyud‐Din, Ahmet Yıldırım and Sefa Anıl Sezer

The purpose of this paper is to use the homotopy perturbation method (HPM) to obtain numerical soliton solution of the improved Boussinesq equation (IBE). The solutions are…

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Abstract

Purpose

The purpose of this paper is to use the homotopy perturbation method (HPM) to obtain numerical soliton solution of the improved Boussinesq equation (IBE). The solutions are calculated in the form of a convergent power series with easily computable components.

Design/methodology/approach

The HPM is used to obtain numerical soliton solution of the IBE. The solutions are calculated in the form of a convergent power series with easily computable components.

Findings

The errors are obtained by using the approximate solution given by using only two iterations of the HPM. It is evident that the efficiency of this approach can be dramatically enhanced by computing further terms of approximate solution.

Originality/value

The numerical results presented in the paper show that only a few terms are sufficient to obtain accurate solutions.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 21 no. 7
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 17 May 2011

Sefa Anıl Sezer, Ahmet Yıldırım and Syed Tauseef Mohyud‐Din

The purpose of this paper is to directly extend the homotopy perturbation method (HPM) that was developed for integer‐order differential equation, to derive explicit and numerical…

396

Abstract

Purpose

The purpose of this paper is to directly extend the homotopy perturbation method (HPM) that was developed for integer‐order differential equation, to derive explicit and numerical solutions of the fractional KdV‐Burgers‐Kuramoto equation.

Design/methodology/approach

The authors used Maple Package to calculate the functions obtained from the HPM.

Findings

The fractional derivatives are described in the Caputo sense. HPM performs extremely well in terms of accuracy, efficiently, simplicity, stability and reliability.

Originality/value

The paper describes how the HPM has been successfully applied to find the solution of fractional KdV‐Burgers‐Kuramoto equation.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 21 no. 4
Type: Research Article
ISSN: 0961-5539

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