Efficient and Robust Methods for Steady-State Patterns in Reaction-Diffusion Systems
نویسندگان
چکیده
Pattern formation is one of the important topics in biological study. The publication of the paper by Turing [8] gave us a big hint for how the biological patterns formed. Turing suggested that some reaction-diffusion systems with suitable range of parameters could give the spatial patterns in concentrations. In his study, the pattern formation is based on the conjunction of local selfenhancement and long-range inhibition which come from the huge difference of diffusion rates of different chemicals. The kind of systems is stiff and there will be big challenges for numerical study.
منابع مشابه
A robust and efficient method for steady state patterns in reaction-diffusion systems
An inhomogeneous steady state pattern of nonlinear reaction-diffusion equations with no-flux boundary conditions is usually computed by solving the corresponding time-dependent reaction-diffusion equations using temporal schemes. Nonlinear solvers (e.g., Newton's method) take less CPU time in direct computation for the steady state; however, their convergence is sensitive to the initial guess, ...
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Article history: Received 16 September 2011 Received in revised form 3 April 2012 Accepted 8 April 2012 Available online 25 April 2012
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