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Changiz Goli Keshavarzi Farideh Ghoreishi

Abstract

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.

Article Details

Keywords

Allen–Cahn equation;, RBF collocation method;, Shifted surface spline;, Stability;, Solvability.

References
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How to Cite
KeshavarziC. G., & GhoreishiF. (2020). Numerical solution of the Allen-Cahn equation by using ”shifted” surface spline radial basis functions. Iranian Journal of Numerical Analysis and Optimization, 10(2), 177-196. https://doi.org/10.22067/ijnao.v10i2.86296
Section
Research Article