Numerical solutions of the reaction-diffusion equation

Numerical solutions of the reaction-diffusion equation 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png International Journal of Numerical Methods for Heat & Fluid Flow Emerald Publishing

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Publisher
Emerald Publishing
Copyright
Copyright © Emerald Group Publishing Limited
ISSN
0961-5539
DOI
10.1108/HFF-04-2014-0113
Publisher site
See Article on Publisher Site

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.

Journal

International Journal of Numerical Methods for Heat & Fluid FlowEmerald Publishing

Published: Mar 2, 2015

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