Unconditionally monotone and globally stable difference schemes for the Fisher equation
https://doi.org/10.29235/1561-8323-2023-67-6-454-459
Abstract
In this paper, we construct and study unconditionally monotone and globally stable difference schemes for the Fisher equation. It has been shown that constructed schemes inherit the stability property of the exact solution: 0 ≤ u(x, t) ≤ 1, (x, t) ∈ QT = {(x, t) : 0 ≤ x ≤ l, 0 ≤ t < +∞} for a given input data of the problem. The unconditional monotonicity of the difference schemes is proved and the a priori estimate is obtained in the uniform norm for the difference solution. The stable behavior of the difference solution in the nonlinear case takes place under slightly more stringent constraints on the input data: 0,5 ≤ u0 (x), µ1(t), µ2(t) ≤ 1.
About the Authors
P. P. Matus
Institute of Mathematics of the National Academy of Sciences of Belarus; Institute of Mathematics and Computer Science the John Paul II Catholic University of Lublin
Belarus
Belarus
Matus Piotr P. – Corresponding Member, D. Sc. (Physics and Mathematics), Professor, Chief Researcher.
11, Surganov Str., 220072, Minsk
D. Pylak
Institute of Mathematics and Computer Science the John Paul II Catholic University of Lublin
Poland
Poland
Pylak Dorota – Assistant Professor.
8, Al. Raclawickie, 20-950, Lublin
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