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Numerical solutions of the reaction-diffusion equation: An integral equation method using the variational iteration method

G Wu (Institute of Applied Nonlinear Science, Neijiang Normal University, Neijiang, China)
Eric Wai Ming Lee (Department of Civil and Architectural Engineering, City University of Hong Kong, Kowloon, Hong Kong)
Gao Li (State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu, China)

International Journal of Numerical Methods for Heat & Fluid Flow

ISSN: 0961-5539

Article publication date: 2 March 2015

Abstract

Purpose

The purpose of this paper is to introduce variational iteration method (VIM) to construct equivalent integral equations for initial-boundary value problems of nonlinear partial differential equations. The Lagrange multipliers become the integral kernels.

Design/methodology/approach

Using the discrete numerical integral formula, the general way is given to solve the famous reaction-diffusion equation numerically.

Findings

With the given explicit solution, the results show the conveniences of the general numerical schemes and numerical simulation of the reaction-diffusion is finally presented in the cases of various coefficients.

Originality/value

The method avoids the treatment of the time derivative as that in the classical finite difference method and the VIM is introduced to construct equivalent integral equations for initial-boundary value problems of nonlinear partial differential equations.

Keywords

Acknowledgements

The work was financially supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. CityU 116613) and the National Natural Science Foundation of China (Grant No. 11301257 and 51104124).

Citation

Wu, G., Lee, E.W.M. and Li, G. (2015), "Numerical solutions of the reaction-diffusion equation: An integral equation method using the variational iteration method", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 25 No. 2, pp. 265-271. https://doi.org/10.1108/HFF-04-2014-0113

Publisher

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Emerald Group Publishing Limited

Copyright © 2015, Emerald Group Publishing Limited