Notes on finite difference schemes to a parabolic-elliptic system modelling chemotaxis

被引：27

作者：

Saito, N

Suzuki, T

机构：

[1] Toyama Univ, Fac Educ, Toyama 9308555, Japan

[2] Osaka Univ, Grad Sch Engn Sci, Div Math Sci, Dept Syst Innovat, Toyonaka, Osaka 5608531, Japan

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2005年 / 171卷 / 01期

关键词：

finite difference scheme; parabolic-elliptic system; positively conservation; mass conservation;

D O I：

10.1016/j.amc.2005.01.037

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider numerical solutions to a nonlinear parabolic-elliptic system in mathematical biology. An important property of solutions to the system is the conservation of L-1 norm. Applying the upwind technique, we make a finite difference scheme satisfying the conservation of a discrete L-1 norm. We also describe a remark on time discretization from the view point of Lyapunov's property which is another important feature of the system. Several numerical examples clarify the nature of our scheme. (c) 2005 Elsevier Inc. All rights reserved.

引用

页码：72 / 90

页数：19

共 11 条

[1]

Biler P., 1998, Adv. Math. Sci. Appl., V8, P715

[2] Finite difference schemes for partial derivativeu/partial derivativet=(partial derivative/partial derivativex)α δG/δu that inherit energy conservation or dissipation property [J].