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 - <p style="text-align: justify;">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.</p>