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Volume 21, Issue 6
A Finite Volume Method Preserving the Invariant Region Property for the Quasimonotone Reaction-Diffusion Systems

Huifang Zhou, Yuchun Sun & Fuchang Huo

DOI: 10.4208/ijnam2024-1036

Int. J. Numer. Anal. Mod., 21 (2024), pp. 910-932.

Published online: 2024-10

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  • 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.

  • Keywords

Reaction-diffusion systems, quasimonotone, nonlinear finite volume scheme, invariant region, distorted meshes, existence, model.

  • AMS Subject Headings

65M08, 35K58

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{IJNAM-21-910, author = {Zhou , HuifangSun , Yuchun and Huo , Fuchang}, title = {A Finite Volume Method Preserving the Invariant Region Property for the Quasimonotone Reaction-Diffusion Systems}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2024}, volume = {21}, number = {6}, pages = {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.

}, issn = {2617-8710}, doi = {https://doi.org/10.4208/ijnam2024-1036}, url = {http://global-sci.org/intro/article_detail/ijnam/23465.html} }
TY - JOUR T1 - A Finite Volume Method Preserving the Invariant Region Property for the Quasimonotone Reaction-Diffusion Systems AU - Zhou , Huifang AU - Sun , Yuchun AU - Huo , Fuchang JO - International Journal of Numerical Analysis and Modeling VL - 6 SP - 910 EP - 932 PY - 2024 DA - 2024/10 SN - 21 DO - http://doi.org/10.4208/ijnam2024-1036 UR - https://global-sci.org/intro/article_detail/ijnam/23465.html KW - Reaction-diffusion systems, quasimonotone, nonlinear finite volume scheme, invariant region, distorted meshes, existence, model. AB -

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.

Zhou , HuifangSun , Yuchun and Huo , Fuchang. (2024). A Finite Volume Method Preserving the Invariant Region Property for the Quasimonotone Reaction-Diffusion Systems. International Journal of Numerical Analysis and Modeling. 21 (6). 910-932. doi:10.4208/ijnam2024-1036
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