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2003 A multigrid method for pattern formation problems in biology
Chiachi Chiu, Hsiu-Chuan Wei
Differential Integral Equations 16(2): 201-220 (2003). DOI: 10.57262/die/1356060684


Mathematical models of many pattern formation problems in biology are reaction-diffusion systems. These systems are important for computer simulations of the patterns, parameter estimations as well as analysis of the biological properties. In order to solve reaction-diffusion systems efficiently, fast and stable numerical algorithms are essential for the pattern formation problems. In this paper, a fairly general reaction-diffusion system is considered. We propose a fully implicit discretization combined with a multigrid V-cycle solver for solving the reaction-diffusion system. Theorems about unconditional stability and convergence of the algorithm are given to show that the algorithm is highly stable and efficient. Numerical experiment results are given for two reaction-diffusion systems that can be used for generating animal coat markings. We also show the comparison results of the multigrid algorithm with other numerical algorithms.


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Chiachi Chiu. Hsiu-Chuan Wei. "A multigrid method for pattern formation problems in biology." Differential Integral Equations 16 (2) 201 - 220, 2003.


Published: 2003
First available in Project Euclid: 21 December 2012

zbMATH: 1024.92002
MathSciNet: MR1947092
Digital Object Identifier: 10.57262/die/1356060684

Primary: 92C15
Secondary: 65M06 , 65M12 , 65M55 , 81T80

Rights: Copyright © 2003 Khayyam Publishing, Inc.

Vol.16 • No. 2 • 2003
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