A Finite Volume Method Preserving the Invariant Region Property for the Quasimonotone Reaction-Diffusion Systems
Year: 2024
Author: Huifang Zhou, Yuchun Sun, Fuchang Huo
International Journal of Numerical Analysis and Modeling, Vol. 21 (2024), Iss. 6 : pp. 910–932
Abstract
We present a finite volume method preserving the invariant region property (IRP) for the reaction-diffusion systems with quasimonotone functions, including nondecreasing, decreasing, and mixed quasimonotone systems. The diffusion terms and time derivatives are discretized using a finite volume method that satisfies the discrete maximum principle (DMP) and the backward Euler method, respectively. The discretization leads to an implicit and nonlinear scheme, and it is proved to preserve the invariant region property unconditionally. We construct an iterative algorithm and prove the invariant region property at each iteration step. Numerical examples are provided to confirm the accuracy and invariant region property of our scheme.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ijnam2024-1036
International Journal of Numerical Analysis and Modeling, Vol. 21 (2024), Iss. 6 : pp. 910–932
Published online: 2024-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 23
Keywords: Reaction-diffusion systems quasimonotone nonlinear finite volume scheme invariant region distorted meshes existence model.
Author Details
Huifang Zhou Email
Yuchun Sun Email
Fuchang Huo Email