报告题目：Strang's Splitting Method for Spatial Fractional Allen-Cahn Equations

报告时间：2023-05-09  10:00 - 11:00

报告人：孙海卫 教授(澳门大学)

报告地点：理学院东北楼三楼会议室

Abstract: In this talk, we study the numerical solutions of the spatial fractional Allen-Cahn equations. After semi-discretization for the spatial fractional Riesz derivative, a system of nonlinear ordinary differential equations with Toeplitz structure is obtained. For the sake of reducing the computational complexity, Strang splitting methods are proposed where the Toeplitz matrix in the system is split into the sum of a circulant matrix and a skew circulant matrix. Therefore, the proposed method can be quickly implemented by the fast Fourier transform, substituting to calculate the expensive Toeplitz matrix exponential. Theoretically, the discrete maximum principle of our method is unconditionally preserved. Moreover, the analysis of error in norms in Banach space with second-order accuracy is conducted in both time and space. Finally, numerical tests are given to corroborate our theoretical conclusions and the efficiency of the proposed method.

　It is a joint work with Yaoyuan Cai, Zhiwei Fang, and Hao Chen.