A Method to Solve the Reaction-Diffusion-Chemotaxis System
-
Yao-Hsin Hwang
and
Chin-Kun Hu
Abstract
The objective of this article is to use a recent developed scheme to simulate reaction-diffusion-chemotaxis equations. The solution gradient required for an accurate discretization is computed directly as an additional variable rather than interpolated from solution values around neighboring computational nodes. To achieve this goal, a supplementary equation and its associated control volume are introduced to retain a compact and accurate discretization. Scheme essentials are exposed by the numerical analysis on two-dimensional chemotaxis problems to reveal its formal accuracy. Due to its highly comprehensible and practical features, this formulation can be easily extended to solve problems for other two-dimensional rectangular grid systems. One- and two-dimensional problems are solved to verify its simulation accuracy and to study the possible formation of bacteria bands. We further perform the linearization technique to the reaction term to increase the stability of the current scheme. From the numerical analysis and computational results, it is found that the present formulation is a useful tool to solve reaction-diffusion-chemotaxis equations.
Funding source: Ministry of Science and Technology, Taiwan
Award Identifier / Grant number: 104-2115-M-126-001 and 107-2112-M-259-006
Funding statement: This work was supported by the Ministry of Science and Technology, Taiwan (Funder ID: http://doi.org/10.13039/501100004663, Grant Number: MOST 104-2115-M-126-001 and 107-2112-M-259-006).
Acknowledgements
JLY acknowledges the Institute of Physics, Academia Sinica, Taiwan, for her summer visit. The authors are grateful to the reviewers’ valuable comments.
References
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© 2019 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Research article
- Improved Results on Adaptive Control Approach for Projective Synchronization of Neural Networks with Time-Varying Delay
- A Method to Solve the Reaction-Diffusion-Chemotaxis System
- Two-Phase Flow of Fluid-Particle Interaction over a Stretching Sheet in the Presence of Magnetic Field
- An Algorithm for the Approximate Solution of the Fractional Riccati Differential Equation
- Additional Extension of the Mathematical Model for BCG Immunotherapy of Bladder Cancer and Its Validation by Auxiliary Tool
- Extended Transformed Rational Function Method to Nonlinear Evolution Equations
- Approximation of p-Biharmonic Problem using WEB-Spline based Mesh-Free Method
- Lie Symmetries, One-Dimensional Optimal System and Group Invariant Solutions for the Ripa System
- On the Numerical Computation of the Mittag–Leffler Function
Articles in the same Issue
- Frontmatter
- Research article
- Improved Results on Adaptive Control Approach for Projective Synchronization of Neural Networks with Time-Varying Delay
- A Method to Solve the Reaction-Diffusion-Chemotaxis System
- Two-Phase Flow of Fluid-Particle Interaction over a Stretching Sheet in the Presence of Magnetic Field
- An Algorithm for the Approximate Solution of the Fractional Riccati Differential Equation
- Additional Extension of the Mathematical Model for BCG Immunotherapy of Bladder Cancer and Its Validation by Auxiliary Tool
- Extended Transformed Rational Function Method to Nonlinear Evolution Equations
- Approximation of p-Biharmonic Problem using WEB-Spline based Mesh-Free Method
- Lie Symmetries, One-Dimensional Optimal System and Group Invariant Solutions for the Ripa System
- On the Numerical Computation of the Mittag–Leffler Function
