Rational approximation solution of the foam drainage equation with time‐ and space‐fractional derivatives

Abstract

Purpose

The purpose of this paper is to implement the variational iteration method and the homotopy perturbation method to give a rational approximation solution of the foam drainage equation with time‐ and space‐fractional derivatives.

Design/methodology/approach

The fractional derivatives are described in the Caputo sense. In these schemes, the solution takes the form of a convergent series with easily computable components.

Findings

Numerical examples are given to demonstrate the effectiveness of the present methods.

Originality/value

Results show that the proposed schemes are very effective and convenient for solving linear and nonlinear fractional differential equations with high accuracy.

Citation

Yıldırım, A. and Koçak, H. (2012), "Rational approximation solution of the foam drainage equation with time‐ and space‐fractional derivatives", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 22 No. 4, pp. 512-525. https://doi.org/10.1108/09615531211215792