Positivity preserving finite volume scheme for the Nagumo-type equations on distorted meshes

被引：5

作者：

Zhou, Huifang ^{[1
]}

Sheng, Zhiqiang ^{[2
]}

Yuan, Guangwei ^{[2
]}

机构：

[1] China Acad Engn Phys, Grad Sch, POB 2101, Beijing 100088, Peoples R China

[2] Inst Appl Phys & Computat Math, Lab Computat Phys, Beijing, Peoples R China

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2018年 / 336卷

基金：

中国国家自然科学基金;

关键词：

Positivity; Finite volume; Nagumo equation; Distorted meshes; BURGERS-HUXLEY EQUATION; TRAVELING-WAVE SOLUTIONS; DIFFUSION-EQUATIONS; NUMERICAL-SOLUTION; POLYGONAL MESHES; DIFFERENCE SCHEME; BOUNDED SOLUTIONS; MONOTONE; DISCRETIZATION; EXISTENCE;

D O I：

10.1016/j.amc.2018.04.058

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we present a nonlinear positivity preserving finite volume scheme for the Nagumo-type equations with anisotropic tensor diffusion coefficient. For the diffusion term, we use the positivity preserving finite volume scheme. For the time direction, we use the backward Euler approximation. We deal with nonlinear reaction term implicitly and decompose nonlinear reaction coefficient into two nonnegative functions. Thus we get a system of nonlinear algebraic equations. The advantages of our scheme are that it can be applied to distorted meshes and has no severe constraint on the time step. The numerical results verify the theoretical result. (C) 2018 Elsevier Inc. All rights reserved.

引用

页码：182 / 192

页数：11

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