A Local Integral Equation Formulation Based on Moving Kriging Interpolation for Solving Coupled Nonlinear Reaction-Diffusion Equations
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...
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Wiley
2014-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2014/196041 |
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| author | Kanittha Yimnak Anirut Luadsong |
| author_facet | Kanittha Yimnak Anirut Luadsong |
| author_sort | Kanittha Yimnak |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-3ec5bba16700409daf5d9ec91c09b4d2 |
| institution | OA Journals |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
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| series | Advances in Mathematical Physics |
| spelling | doaj-art-3ec5bba16700409daf5d9ec91c09b4d22025-08-20T02:08:20ZengWileyAdvances in Mathematical Physics1687-91201687-91392014-01-01201410.1155/2014/196041196041A Local Integral Equation Formulation Based on Moving Kriging Interpolation for Solving Coupled Nonlinear Reaction-Diffusion EquationsKanittha Yimnak0Anirut Luadsong1Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha-utid Road, Bangmod, Toongkru, Bangkok 10140, ThailandDepartment of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha-utid Road, Bangmod, Toongkru, Bangkok 10140, ThailandThe 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.http://dx.doi.org/10.1155/2014/196041 |
| spellingShingle | Kanittha Yimnak Anirut Luadsong A Local Integral Equation Formulation Based on Moving Kriging Interpolation for Solving Coupled Nonlinear Reaction-Diffusion Equations Advances in Mathematical Physics |
| title | A Local Integral Equation Formulation Based on Moving Kriging Interpolation for Solving Coupled Nonlinear Reaction-Diffusion Equations |
| title_full | A Local Integral Equation Formulation Based on Moving Kriging Interpolation for Solving Coupled Nonlinear Reaction-Diffusion Equations |
| title_fullStr | A Local Integral Equation Formulation Based on Moving Kriging Interpolation for Solving Coupled Nonlinear Reaction-Diffusion Equations |
| title_full_unstemmed | A Local Integral Equation Formulation Based on Moving Kriging Interpolation for Solving Coupled Nonlinear Reaction-Diffusion Equations |
| title_short | A Local Integral Equation Formulation Based on Moving Kriging Interpolation for Solving Coupled Nonlinear Reaction-Diffusion Equations |
| title_sort | local integral equation formulation based on moving kriging interpolation for solving coupled nonlinear reaction diffusion equations |
| url | http://dx.doi.org/10.1155/2014/196041 |
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