Fractional step methods applied to a chemotaxis model

A fractional step numerical method is developed for the nonlinear partial differential equations arising in chemotaxis models, which include density-dependent diffusion terms for chemotaxis, as well as reaction and Fickian diffusion terms. We take the novel approach of viewing the chemotaxis term as...

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Bibliographic Details
Published in:Journal of mathematical biology 2000-11, Vol.41 (5), p.455-475
Main Authors: Tyson, R, Stern, L G, LeVeque, R J
Format: Article
Language:English
Subjects:
Chemotaxis - physiology
Computer Simulation
Escherichia coli - growth & development
Escherichia coli - physiology
Models, Biological
Salmonella typhimurium - growth & development
Salmonella typhimurium - physiology
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Summary:A fractional step numerical method is developed for the nonlinear partial differential equations arising in chemotaxis models, which include density-dependent diffusion terms for chemotaxis, as well as reaction and Fickian diffusion terms. We take the novel approach of viewing the chemotaxis term as an advection term which is possible in the context of fractional steps. This method is applied to pattern formation problems in bacterial growth and shown to give good results. High-resolution methods capable of capturing steep gradients (from CLAWPACK) are used for the advection step, while the A-stable and L-stable TR-BDF2 method is used for the diffusion step. A numerical instability that is seen with other diffusion methods is analyzed and eliminated.
ISSN:0303-6812
1432-1416
DOI:10.1007/s002850000038