Numerical approximation of one model of bacterial self-organization
This paper presents finite difference approximations of one dimensional in space mathematical model of a bacterial self-organization. The dynamics of such nonlinear systems can lead to formation of complicated solution patterns. In this paper we show that this chemotaxisdriven instability can be co...
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Vilnius University Press
2012-07-01
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doaj-6d29812fa22e45589296def2f773cc402020-11-25T00:49:03ZengVilnius University PressNonlinear Analysis1392-51132335-89632012-07-01173Numerical approximation of one model of bacterial self-organizationRaimondas Čiegis0Andrej Bugajev1Vilnius Gediminas Technical University, LithuaniaVilnius Gediminas Technical University, Lithuania This paper presents finite difference approximations of one dimensional in space mathematical model of a bacterial self-organization. The dynamics of such nonlinear systems can lead to formation of complicated solution patterns. In this paper we show that this chemotaxisdriven instability can be connected to the ill-posed problem defined by the backward in time diffusion process. The method of lines is used to construct robust numerical approximations. At the first step we approximate spatial derivatives in the PDE by applying approximations targeted for special physical processes described by differential equations. The obtained system of ODE is split into a system describing separately fast and slow physical processes and different implicit and explicit numerical solvers are constructed for each subproblem. Results of numerical experiments are presented and convergence of finite difference schemes is investigated. http://www.journals.vu.lt/nonlinear-analysis/article/view/14054finite difference methoddiffusion-advection-reaction modelssplitting schemesstabilityconvergencebackward-time parabolic problem |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Raimondas Čiegis Andrej Bugajev |
spellingShingle |
Raimondas Čiegis Andrej Bugajev Numerical approximation of one model of bacterial self-organization Nonlinear Analysis finite difference method diffusion-advection-reaction models splitting schemes stability convergence backward-time parabolic problem |
author_facet |
Raimondas Čiegis Andrej Bugajev |
author_sort |
Raimondas Čiegis |
title |
Numerical approximation of one model of bacterial self-organization |
title_short |
Numerical approximation of one model of bacterial self-organization |
title_full |
Numerical approximation of one model of bacterial self-organization |
title_fullStr |
Numerical approximation of one model of bacterial self-organization |
title_full_unstemmed |
Numerical approximation of one model of bacterial self-organization |
title_sort |
numerical approximation of one model of bacterial self-organization |
publisher |
Vilnius University Press |
series |
Nonlinear Analysis |
issn |
1392-5113 2335-8963 |
publishDate |
2012-07-01 |
description |
This paper presents finite difference approximations of one dimensional in space mathematical model of a bacterial self-organization. The dynamics of such nonlinear systems can lead to formation of complicated solution patterns. In this paper we show that this chemotaxisdriven instability can be connected to the ill-posed problem defined by the backward in time diffusion process. The method of lines is used to construct robust numerical approximations. At the first step we approximate spatial derivatives in the PDE by applying approximations targeted for special physical processes described by differential equations. The obtained system of ODE is split into a system describing separately fast and slow physical processes and different implicit and explicit numerical solvers are constructed for each subproblem. Results of numerical experiments are presented and convergence of finite difference schemes is investigated.
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topic |
finite difference method diffusion-advection-reaction models splitting schemes stability convergence backward-time parabolic problem |
url |
http://www.journals.vu.lt/nonlinear-analysis/article/view/14054 |
work_keys_str_mv |
AT raimondasciegis numericalapproximationofonemodelofbacterialselforganization AT andrejbugajev numericalapproximationofonemodelofbacterialselforganization |
_version_ |
1725253259729305600 |