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A finite difference method for modeling the formation of animal coat patterns

Authors
Journal
Nonlinear Analysis Real World Applications
1468-1218
Publisher
Elsevier
Publication Date
Volume
10
Issue
3
Identifiers
DOI: 10.1016/j.nonrwa.2008.02.012
Keywords
  • Reaction–Diffusion System
  • Mathematical Biology
  • Peaceman–Rachford
  • Finite Difference Method
Disciplines
  • Mathematics

Abstract

Abstract We consider a nonlinear reaction–diffusion system for the formation of animal coat patterns proposed by J.D. Murray. We approximate the nonlinear partial differential equations by an extension of the Peaceman–Rachford finite difference method for linear equations. We then run experiments where we execute our method until steady-state is reached to obtain a variety of animal coat patterns.

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