A maximum bound principle preserving iteration technique for a class of semilinear parabolic equations

This paper presents a systematic methodology, called the MBP-preserving iteration technique, to develop the maximum bound principle (MBP) preserving numerical algorithms for a class of semilinear parabolic equations. Two types of MBP-preserving iterations are suggested to solve two well-known θ-weig...

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Bibliographic Details
Published in:Applied numerical mathematics 2023-02, Vol.184, p.482-495
Main Authors: Gong, Yuezheng, Ji, Bingquan, Liao, Hong-lin
Format: Article
Language:English
Subjects:
Adaptive time-stepping strategy
Error estimate
Maximum bound principle
MBP-preserving iteration technique
Semilinear parabolic equations
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Summary:This paper presents a systematic methodology, called the MBP-preserving iteration technique, to develop the maximum bound principle (MBP) preserving numerical algorithms for a class of semilinear parabolic equations. Two types of MBP-preserving iterations are suggested to solve two well-known θ-weighted schemes, respectively. Within some mild time-step constraints, the corresponding iteration solutions are proved to preserve the MBP property at each iteration step so that the numerical scheme has a uniquely MBP-preserving solution. In addition, concise error estimates in the maximum norm are established on nonuniform time meshes. Several numerical examples coupled with an adaptive time-stepping strategy are implemented for the Allen-Cahn model to confirm the theoretical findings and demonstrate their effectiveness for long-time numerical simulations.
ISSN:0168-9274
1873-5460
DOI:10.1016/j.apnum.2022.11.002