NDLI: Asymptotic High Order Mass-Preserving Schemes for a Hyperbolic Model of Chemotaxis

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Natalini, R. Ribot, M.
Copyright Year	2012
Abstract	We introduce a new class of finite difference schemes for approximating the solutions to an initial-boundary value problem on a bounded interval for a one-dimensional dissipative hyperbolic system with an external source term, which arises as a simple model of chemotaxis. Since the solutions to this problem may converge to nonconstant asymptotic states for large times, standard schemes usually fail to yield a good approximation. Therefore, we propose a new class of schemes, which use an asymptotic higher order correction, second and third order in our examples, to balance the effects of the source term and the influence of the asymptotic solutions. Special care is needed to deal with boundary conditions to avoid harmful loss of mass. Convergence results are proved for these new schemes, and several numerical tests are presented and discussed to verify the effectiveness of their behavior.
Starting Page	883
Ending Page	905
Page Count	23
File Format	PDF
ISSN	00361429
DOI	10.1137/100803067
e-ISSN	10957170
Issue Number	2
Volume Number	50
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2012-04-17
Access Restriction	Subscribed
Subject Keyword	Initial-boundary value problems for first-order hyperbolic systems asymptotic behavior General biology and biomathematics finite difference schemes Cell movement initial-boundary value problem Nonlinear first-order hyperbolic equations hyperbolic systems with source chemotaxis Finite difference methods
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Numerical Analysis Computational Mathematics

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