Differential and Integral Equations

A multigrid method for pattern formation problems in biology

Chiachi Chiu and Hsiu-Chuan Wei

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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.

Article information

Differential Integral Equations, Volume 16, Number 2 (2003), 201-220.

First available in Project Euclid: 21 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 92C15: Developmental biology, pattern formation
Secondary: 65M06: Finite difference methods 65M12: Stability and convergence of numerical methods 65M55: Multigrid methods; domain decomposition 81T80: Simulation and numerical modeling


Chiu, Chiachi; Wei, Hsiu-Chuan. A multigrid method for pattern formation problems in biology. Differential Integral Equations 16 (2003), no. 2, 201--220. https://projecteuclid.org/euclid.die/1356060684

Export citation