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Article
Publication date: 8 June 2012

Mehdi Dehghan and Jalil Manafian Heris

This paper aims to show that the variational iteration method (VIM) and the homotopy perturbation method (HPM) are powerful and suitable methods to solve the…

Abstract

Purpose

This paper aims to show that the variational iteration method (VIM) and the homotopy perturbation method (HPM) are powerful and suitable methods to solve the Fornberg‐Whitham equation.

Design/methodology/approach

Using HPM the explicit exact solution is calculated in the form of a quickly convergent series with easily computable components. Also, by using VIM the analytical results of this equation have been obtained in terms of convergent series with easily computable components.

Findings

Numerical solutions obtained by these methods are compared with the exact solutions, revealing that the obtained solutions are of high accuracy.

Originality/value

Also the results show that the introduced methods are efficient tools for solving the nonlinear partial differential equations.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 22 no. 5
Type: Research Article
ISSN: 0961-5539

Keywords

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Article
Publication date: 9 August 2011

Mehdi Dehghan, Jalil Manafian Heris and Abbas Saadatmandi

The purpose of this paper is to use He's Exp‐function method (EFM) to construct solitary and soliton solutions of the nonlinear evolution equation.

Abstract

Purpose

The purpose of this paper is to use He's Exp‐function method (EFM) to construct solitary and soliton solutions of the nonlinear evolution equation.

Design/methodology/approach

This technique is straightforward and simple to use and is a powerful method to overcome some difficulties in the nonlinear problems.

Findings

This method is developed for searching exact traveling wave solutions of the nonlinear partial differential equations. The EFM presents a wider applicability for handling nonlinear wave equations.

Originality/value

The paper shows that EFM, with the help of symbolic computation, provides a straightforward and powerful mathematical tool for solving nonlinear evolution equations. Application of EFM to Fitzhugh‐Nagumo equation illustrates its effectiveness.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 21 no. 6
Type: Research Article
ISSN: 0961-5539

Keywords

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