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Numerical investigation based on a local meshless radial point interpolation for solving coupled nonlinear reaction-diffusion system | ||
| Computational Methods for Differential Equations | ||
| مقاله 3، دوره 9، شماره 2، تیر 2021، صفحه 358-374 اصل مقاله (1.11 MB) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2019.30396.1450 | ||
| نویسندگان | ||
Elyas Shivanian  ؛ Ahmad Jafarabadi
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| Department of Applied Mathematics, Imam Khomeini International University, Qazvin, 34149-16818, Iran. | ||
| چکیده | ||
| In the present paper, the spectral meshless radial point interpolation (SMRPI) technique is applied to the solution of pattern formation in nonlinear reaction-diffusion systems. Firstly, we obtain a time discrete scheme by approximating the time derivative via a finite difference formula, then we use the SMRPI approach to approximate the spatial derivatives. This method is based on a combination of meshless methods and spectral collocation techniques. The point interpolation method with the help of radial basis functions is used to construct shape functions which act as basis functions in the frame of SMRPI. In the current work, the thin plate splines (TPS) are used as the basis functions and in order to eliminate the nonlinearity, a simple predictor-corrector (P-C) scheme is performed. The effect of parameters and conditions are studied by considering the well known Brusselator model. Two test problems are solved and numerical simulations are reported which confirm the efficiency of the proposed scheme. | ||
| کلیدواژهها | ||
| Turing systems؛ Brusselator model؛ Spectral meshless radial point interpolation (SMRPI) method؛ Radial basis function, Finite difference method | ||
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آمار تعداد مشاهده مقاله: 317 تعداد دریافت فایل اصل مقاله: 309 |
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