Numerical solution of the Allen-Cahn equation by using ”shifted” surface spline radial basis functions
عنوان مقاله: Numerical solution of the Allen-Cahn equation by using ”shifted” surface spline radial basis functions
شناسه ملی مقاله: JR_IJNAO-10-2_009
منتشر شده در در سال 1399
شناسه ملی مقاله: JR_IJNAO-10-2_009
منتشر شده در در سال 1399
مشخصات نویسندگان مقاله:
Changiz Goli Keshavarzi - Department of Mathematics, K. N. Toosi University of Technology, Tehran, Iran.
Farideh Ghoreishi - Department of Mathematics, K. N. Toosi University of Technology, Tehran, Iran
خلاصه مقاله:
Changiz Goli Keshavarzi - Department of Mathematics, K. N. Toosi University of Technology, Tehran, Iran.
Farideh Ghoreishi - Department of Mathematics, K. N. Toosi University of Technology, Tehran, Iran
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.
کلمات کلیدی: Allen–Cahn equation, RBF collocation method, Shifted surface spline, Stability, Solvability
صفحه اختصاصی مقاله و دریافت فایل کامل: https://civilica.com/doc/1170456/