A numerical simulation of modified Boussinesq and seven‐order Sawada‐Kotara equations

Abstract

Purpose

The purpose of this paper is to apply the variational iterations method to solve two difference types such as the modified Boussinesq (MB) and seven‐order Sawada‐Kotara (sSK) equations and to compare this method with that obtained previously by Adomian decomposition.

Design/methodology/approach

The variational iteration method is used for finding the solution of the MB and sSK equations. The solution obtained is an infinite power series for appropriate initial condition. The numerical results obtain for nth approximation and compare with the known analytical solutions; the results show that an excellent approximation to the actual solution of the equations was achieved by using only three iterations.

Findings

The comparison demonstrates that the two obtained solutions are an excellent agreement. The numerical results calculated show that this method, variational iteration method, can be readily implemented to this type of nonlinear equation and excellent accuracy can be achieved. The results of variation iteration method confirm the correctness of those obtained by means of Adomian decomposition method.

Originality/value

The results presented in this paper show that the variational iteration method is a powerful mathematical tool for solving the MB and the sSK equations; it is also a promising method for solving other nonlinear equations.

Citation

Soliman, A.A. (2011), "A numerical simulation of modified Boussinesq and seven‐order Sawada‐Kotara equations", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 21 No. 3, pp. 320-330. https://doi.org/10.1108/09615531111108495