北华大学学报（自然科学版）2026，Vol.27Issue(2)：173-179,7.DOI:10.11713/j.issn.1009-4822.2026.02.001
具有周期边界条件的三元Allen-Cahn方程的数值分析
Numerical Analysis of Ternary Allen-Cahn Equations with Periodic Boundary Conditions
摘要
Abstract
A second-order linear finite difference scheme is proposed for solving the ternary Allen-Cahn equa-tion,which employs a leap-frog difference scheme with a stabilization term for temporal discretization and a sec-ond-order central difference method for spatial discretization.It is proven that the numerical solution satisfies the discrete maximum principle under reasonable time step sizes and restrictions on the stabilization term coefficients.Based on the maximum principle,the infinity norm error is analyzed,and numerical examples are provided to ver-ify the theoretical results.关键词
三元Allen-Cahn方程/有限差分方法/极大值原理/误差估计Key words
ternary Allen-Cahn equation/finite difference method/maximum principle/error estimate分类
数理科学引用本文复制引用
王梓安,侯天亮..具有周期边界条件的三元Allen-Cahn方程的数值分析[J].北华大学学报（自然科学版）,2026,27(2):173-179,7.基金项目
吉林省自然科学基金项目(20230101279JC). （20230101279JC）
