A Local Integral Equation Formulation Based on Moving Kriging Interpolation for Solving Coupled Nonlinear Reaction-Diffusion Equations. (4th June 2014)

• Record Type: Journal Article
• Authors: Yimnak, Kanittha; Luadsong, Anirut
• Other Names: Makinde Oluwole Daniel Academic Editor.
• Is Part Of: Advances in mathematical physics. Volume 2014(2014)
• Publication Date: 2014-06-04
• Subjects: Mathematical physics -- Periodicals; Mathematical physics; Periodicals; 530.15
• DOI: 10.1155/2014/196041
• Languages: English
• ISSNs: 1687-9120

Abstract

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.