求解一维Allen-Cahn方程的保能量耗散Du Fort-Frankel格式
Energy Dissipation Du Fort-Frankel Scheme for 1D Allen-Cahn Equation
DOI: 10.12677/PM.2023.1310316, PDF,    国家自然科学基金支持
作者: 梁雨欣：南昌航空大学，数学与信息科学学院，江西 南昌
关键词: Allen-Cahn方程；Du Fort-Frankel格式；离散能量稳定性；Allen-Cahn Equation； Du Fort-Frankel Scheme； Energy Stability
摘要: Allen-Cahn方程的保结构算法常常是全隐线性格式或全隐非线性格式。为提高计算效率，本文提出一类显式Du Fort-Frankel格式，所得数值解保持能量耗散定律。最后，数值结果验证了格式的有效性和保能量耗散性，同时在空间网格为h，时间步长τ = h2的情况下，得到数值解具有二阶的收敛精度。
Abstract: The structure-preserving algorithms for the Allen-Cahn equation are often fully implicit linear schemes or fully implicit nonlinear schemes. To improve computational efficiency, a class of explicit Du Fort-Frankel (DFF) schemes, whose numerical solutions inherit the energy dissipation law is proposed in this study. Finally, numerical results verify the validity and energy dissipation of the scheme. At the same time, under the condition of space grid h and time step τ = h2, the numerical solutions converge to exact solution with an order of O(h2).
文章引用：梁雨欣. 求解一维Allen-Cahn方程的保能量耗散Du Fort-Frankel格式[J]. 理论数学, 2023, 13(10): 3061-3070. https://doi.org/10.12677/PM.2023.1310316

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