Study of the wave‐breaking's qualitative behavior of the Fornberg‐Whitham equation via quasi‐numeric approaches

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.

Citation

Dehghan, M. and Manafian Heris, J. (2012), "Study of the wave‐breaking's qualitative behavior of the Fornberg‐Whitham equation via quasi‐numeric approaches", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 22 No. 5, pp. 537-553. https://doi.org/10.1108/09615531211231235