UNCONDITIONALLY MONOTONE AND GLOBALLY STABLE DIFFERENCE SCHEMES FOR THE FISHER EQUATION

被引：0

作者：

Matus, Piotr P. ^{[1
]}

Pylak, D. ^{[2
]}

机构：

[1] Natl Acad Sci Belarus, Inst Math, 11,Surganov Str, Minsk 220072, BELARUS

[2] John Paul II Catholic Univ Lublin, Inst Math & Comp Sci, 8,Al Raclawickie, PL-20950 Lublin, Poland

来源：

DOKLADY NATSIONALNOI AKADEMII NAUK BELARUSI | 2023年 / 67卷 / 06期

关键词：

unconditional monotonicity; global stability; difference scheme; Fisher equation;

D O I：

10.29235/1561-8323-2023-67-6-454-459

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

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) is an element of (Q) over bar (T) ={(x,t): 0 <= x <= l , 0 <= t< +infinity 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 <= u(0) (x), mu(1) (t), mu(2) (t) <= 1.

引用

页码：454 / 459

页数：6

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