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

DOI10.1016/j.amc.2005.01.037zbMath1086.65089OpenAlexW2156898682MaRDI QIDQ814697

Takashi Suzuki, Norikazu Saito

Publication date: 7 February 2006

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2005.01.037

zbMATH Keywords

chemotaxisfinite difference schemesparabolic-elliptic systemMass conservationpositivity conservation

Mathematics Subject Classification ID

Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.) (92C45) PDEs of mixed type (35M10) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06)

Related Items (17)

A time semi-exponentially fitted scheme for chemotaxis-growth models ⋮ Semi-implicit finite volume schemes for a chemotaxis-growth model ⋮ A corrected decoupled scheme for chemotaxis models ⋮ Stochastic particle approximation for measure valued solutions of the 2D Keller-Segel system ⋮ A numerical algorithm for blow-up problems revisited ⋮ Positivity-preserving high-order compact difference method for the Keller-Segel chemotaxis model ⋮ A survey on well-balanced and asymptotic preserving schemes for hyperbolic models for chemotaxis ⋮ Blow-up dynamics for the aggregation equation with degenerate diffusion ⋮ Finite volume methods for a Keller-Segel system: discrete energy, error estimates and numerical blow-up analysis ⋮ Unnamed Item ⋮ Finite element analysis of a Keller-Segel model with additional cross-diffusion and logistic source. I: Space convergence ⋮ An analysis on the finite volume schemes and the discrete Lyapunov inequalities for the chemotaxis system ⋮ Keller-Segel chemotaxis models: a review ⋮ Numerical study of vanishing and spreading dynamics of chemotaxis systems with logistic source and a free boundary ⋮ Convergence of a Stochastic Particle Approximation for Measure Solutions of the 2D Keller-Segel System ⋮ Energy and implicit discretization of the Fokker-Planck and Keller-Segel type equations ⋮ Two positivity preserving flux limited, second-order numerical methods for a haptotaxis model

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Free energy and self-interacting particles
• Initiation of slime mold aggregation viewed as an instability
• A finite difference approach to the number of peaks of solutions for semilinear parabolic problems
• Finite difference schemes for \(\frac{\partial u}{\partial t}=(\frac{\partial}{\partial x})^\alpha\frac{\delta G}{\delta u}\) that inherit energy conservation or dissipation property
• Conservative upwind finite-element method for a simplified Keller–Segel system modelling chemotaxis

This page was built for publication: Notes on finite difference schemes to a parabolic-elliptic system modelling chemotaxis