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Advances in Mathematical Physics
Volume 2014 (2014), Article ID 196041, 7 pages
http://dx.doi.org/10.1155/2014/196041
Research Article

A Local Integral Equation Formulation Based on Moving Kriging Interpolation for Solving Coupled Nonlinear Reaction-Diffusion Equations

Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha-utid Road, Bangmod, Toongkru, Bangkok 10140, Thailand

Received 5 April 2014; Revised 21 May 2014; Accepted 21 May 2014; Published 4 June 2014

Academic Editor: Oluwole Daniel Makinde

Copyright © 2014 Kanittha Yimnak and Anirut Luadsong. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The meshless local Pretrov-Galerkin method (MLPG) with the test function in view of the Heaviside step function is introduced to solve the system of coupled nonlinear reaction-diffusion equations in two-dimensional spaces subjected to Dirichlet and Neumann boundary conditions on a square domain. Two-field velocities are approximated by moving Kriging (MK) interpolation method for constructing nodal shape function which holds the Kronecker delta property, thereby enhancing the arrangement nodal shape construction accuracy, while the Crank-Nicolson method is chosen for temporal discretization. The nonlinear terms are treated iteratively within each time step. The developed formulation is verified in two numerical examples with investigating the convergence and the accuracy of numerical results. The numerical experiments revealing the solutions by the developed formulation are stable and more precise.