A new linearized maximum principle preserving and energy stability scheme for the space fractional Allen-Cahn equation

被引：0
作者：
Biao Zhang
Yin Yang
机构：
[1] School of Mathematics and Computational Science,
[2] Xiangtan University,undefined
[3] Hunan Key Laboratory for Computation and Simulation in Science and Engineering,undefined
[4] Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education,undefined
[5] School of Mathematics and Computational Science,undefined
[6] Xiangtan University,undefined
[7] National Center for Applied Mathematics in Hunan,undefined
[8] Hunan International Scientific and Technological Innovation Cooperation Base of Computational Science,undefined
来源：
Numerical Algorithms | 2023年 / 93卷
关键词：
Space fractional Allen-Cahn equation; New linearized two-level scheme; Newton linearized technology; Discrete maximum principle; Energy stability; Error analysis;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, a numerical method is proposed to solve the space fractional Allen-Cahn equation. Based on Crank-Nicolson method for time discretization and second-order weighted and shifted Grünwald difference formula for spatial discretization, we present a new linearized two-level scheme, where the nonlinear term is handled by Newton linearized technology. And we only need to solve a linear system at each time level. Then, the unique solvability of the numerical scheme is given. Under the appropriate assumptions of time step, the discrete maximum principle and energy stability of the numerical scheme are proved. Furthermore, we give a detailed error analysis, which reflects that the temporal and spatial convergence orders are both second order. At last, some numerical experiments show that the proposed method is reasonable and effective.
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页码：179 / 202
页数：23
相关论文
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