Finite difference approximation with ADI scheme for two-dimensional Keller-Segel equations

Nonlinear parabolic equations (35K55) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Computational methods for problems pertaining to biology (92-08) Cell movement (chemotaxis, etc.) (92C17) Nonlinear initial, boundary and initial-boundary value problems for nonlinear parabolic equations (35K61)

Cites Work

Finite volume methods for a Keller-Segel system: discrete energy, error estimates and numerical blow-up analysis
Fully discrete analysis of a discontinuous finite element method for the keller-segel chemotaxis model
Numerical approximations of Allen-Cahn and Cahn-Hilliard equations
Initiation of slime mold aggregation viewed as an instability
Traveling bands of chemotactic bacteria: a theoretical analysis
The parabolic-parabolic Keller-Segel model in \(\mathbb R^2\)
A second-order positivity preserving central-upwind scheme for chemotaxis and haptotaxis models
A user's guide to PDE models for chemotaxis
From 1970 until present: The Keller-Segel model in chemotaxis and its consequences. I
Linear, first and second-order, unconditionally energy stable numerical schemes for the phase field model of homopolymer blends
Local discontinuous Galerkin method for the Keller-Segel chemotaxis model
Upwind-difference potentials method for Patlak-Keller-Segel chemotaxis model
Efficient, positive, and energy stable schemes for multi-d Poisson-Nernst-Planck systems
Unconditionally positivity preserving and energy dissipative schemes for Poisson-Nernst-Planck equations
A dynamic mass transport method for Poisson-Nernst-Planck equations
Energy and implicit discretization of the Fokker-Planck and Keller-Segel type equations
Numerical study of two-species chemotaxis models
Random walk with persistence and external bias
The Global Dynamics of Discrete Semilinear Parabolic Equations
Positivity-preserving and asymptotic preserving method for 2D Keller-Segal equations
Bound/Positivity Preserving and Energy Stable Scalar auxiliary Variable Schemes for Dissipative Systems: Applications to Keller--Segel and Poisson--Nernst--Planck Equations
Unconditionally Bound Preserving and Energy Dissipative Schemes for a Class of Keller--Segel Equations
A Variational Lagrangian Scheme for a Phase-Field Model: A Discrete Energetic Variational Approach
A New Class of Efficient and Robust Energy Stable Schemes for Gradient Flows
Toward a mathematical theory of Keller–Segel models of pattern formation in biological tissues
Numerical approximations for a phase field dendritic crystal growth model based on the invariant energy quadratization approach
New Interior Penalty Discontinuous Galerkin Methods for the Keller–Segel Chemotaxis Model
A Finite-Volume Method for Nonlinear Nonlocal Equations with a Gradient Flow Structure
A finite volume scheme for a Keller-Segel model with additional cross-diffusion
A second order accurate, positivity preserving numerical method for the Poisson-Nernst-Planck system and its convergence analysis

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