Numerical solution of the Allen-Cahn equation by using ”shifted” surface spline radial basis functions

Iranian Journal of Numerical Analysis and Optimization

مقاله 9، دوره 10، شماره 2 - شماره پیاپی 18، آذر 2020، صفحه 177-196   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.v10i2.86296

نویسندگان

C.G. Keshavarzi؛ F. Ghoreishi^*

Department of Mathematics, K. N. Toosi University of Technology, Tehran, Iran.

چکیده

We consider a fully-discrete approximation of the Allen-Cahn equation, such that the forward Euler/Crank–Nicolson scheme (in time) combined with the RBF collocation method based on “shifted” surface spline (in space). Numerical solvability and stability of the method, by using second order finite difference matrices are discussed. We show that, in the proposed scheme, the nonlinear term can be treated explicitly and the resultant numerical scheme is linear and easy to implement. Numerical results that show the effciency and reliability of the proposed method are presented, and two types of collocation nodes for solving this equation are compared.

کلیدواژه‌ها

Allen–Cahn equation؛ RBF collocation method؛ Shifted surface spline؛ Stability؛ Solvability

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