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

Iranian Journal of Numerical Analysis and Optimization

Changiz Goli Keshavarzi¹  Farideh Ghoreishi² 

[1] Department of Mathematics, K. N. Toosi University of Technology, Tehran, Iran.;Department of Mathematics, K. N. Toosi University of Technology, Tehran, Iran;

关键词: allen–cahn equation;    rbf collocation method;    shifted surface spline;    stability;    solvability;   

DOI  :  10.22067/ijnao.v10i2.86296

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown