High-order unconditionally maximum-principle-preserving parametric integrating factor Runge-Kutta schemes for the nonlocal Allen-Cahn equation

被引：8

作者：

Gao, Zhongxiong ^{[1
]}

Zhang, Hong ^{[1
]}

Qian, Xu ^{[1
]}

Song, Songhe ^{[1
]}

机构：

[1] Natl Univ Def Technol, Dept Math, Changsha 410073, Hunan, Peoples R China

来源：

APPLIED NUMERICAL MATHEMATICS | 2023年 / 194卷

基金：

中国国家自然科学基金; 国家重点研发计划;

关键词：

Parametric integrating factor Runge-Kutta method; Nonlocal Allen-Cahn equation; Maximum-principle-preservation; ASYMPTOTICALLY COMPATIBLE SCHEMES; FOURIER SPECTRAL APPROXIMATIONS; ROBUST DISCRETIZATION; DIFFUSION; IMPLEMENTATION; MOTION;

D O I：

10.1016/j.apnum.2023.08.010

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We utilize the second-order quadrature-based finite difference method and the high-order parametric integrating factor Runge-Kutta (pIFRK) integrators to construct efficient and accurate schemes for solving the nonlocal Allen-Cahn equation. These schemes preserve the maximum principle for any time-step, and exhibit up to fourth-order accuracy in the temporal direction. We establish a rigorous error estimate and an asymptotic compatibility analysis for the pIFRK schemes. Numerical experiments demonstrate the accuracy and structure-preserving property of the proposed schemes, verify their asymptotic compatibility, and investigate the discontinuity of the nonlocal Allen-Cahn equation under certain conditions. (c) 2023 IMACS. Published by Elsevier B.V. All rights reserved.

引用

页码：97 / 114

页数：18

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