具有周期边界条件的三元Allen-Cahn方程的数值分析OA
Numerical Analysis of Ternary Allen-Cahn Equations with Periodic Boundary Conditions
提出一类求解三元 Allen-Cahn 方程的二阶线性有限差分格式,分别采用带有稳定项的蛙跳差分格式和二阶中心差分方法对时间和空间进行离散.证明了数值解在合理的时间步长以及稳定项系数的限制下满足离散极大值原理,基于极大值原理分析了无穷范数误差,并给出数值算例验证理论结果.
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.
王梓安;侯天亮
北华大学数学与统计学院,吉林 吉林 132013北华大学数学与统计学院,吉林 吉林 132013
数理科学
三元Allen-Cahn方程有限差分方法极大值原理误差估计
ternary Allen-Cahn equationfinite difference methodmaximum principleerror estimate
《北华大学学报（自然科学版）》 2026 (2)
173-179,7
吉林省自然科学基金项目(20230101279JC).
评论