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Adaptive Optimal m-Stage Runge-Kutta Methods for Solving Reaction-Diffusion-Chemotaxis Systems
Author
Source
Journal of Applied Mathematics
Issue
Vol. 2011, Issue 2011 (31 Dec. 2011), pp.1-25, 25 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2011-06-28
Country of Publication
Egypt
No. of Pages
25
Main Subjects
Abstract EN
We present a class of numerical methods for the reaction-diffusion-chemotaxis system which is significant for biological and chemistry pattern formation problems.
To solve reaction-diffusion-chemotaxis systems, efficient and reliable numerical algorithms are essential for pattern generations.
Along with the implementation of the method of lines, implicit or semi-implicit schemes are typical time stepping solvers to reduce the effect on time step constrains due to the stability condition.
However, these two schemes are usually difficult to employ.
In this paper, we propose an adaptive optimal time stepping strategy for the explicit m-stage Runge-Kutta method to solve reaction-diffusion-chemotaxis systems.
Instead of relying on empirical approaches to control the time step size, variable time step sizes are given explicitly.
Yet, theorems about stability and convergence of the algorithm are provided in analyzing robustness and efficiency.
Numerical experiment results on a testing problem and a real application problem are shown.
American Psychological Association (APA)
Yu, Jui-Ling. 2011. Adaptive Optimal m-Stage Runge-Kutta Methods for Solving Reaction-Diffusion-Chemotaxis Systems. Journal of Applied Mathematics،Vol. 2011, no. 2011, pp.1-25.
https://search.emarefa.net/detail/BIM-468210
Modern Language Association (MLA)
Yu, Jui-Ling. Adaptive Optimal m-Stage Runge-Kutta Methods for Solving Reaction-Diffusion-Chemotaxis Systems. Journal of Applied Mathematics No. 2011 (2011), pp.1-25.
https://search.emarefa.net/detail/BIM-468210
American Medical Association (AMA)
Yu, Jui-Ling. Adaptive Optimal m-Stage Runge-Kutta Methods for Solving Reaction-Diffusion-Chemotaxis Systems. Journal of Applied Mathematics. 2011. Vol. 2011, no. 2011, pp.1-25.
https://search.emarefa.net/detail/BIM-468210
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-468210