A Comparison of Two Numerical Methodsfor Oscillatory Reaction - Di usion SystemsJ

نویسنده

  • J. A. Sherratt
چکیده

|Reaction-diiusion systems whose kinetics contain a stable limit cycle are an established class of models for a range of oscillatory biological and chemical phenomena. In this paper, the author compares two numerical methods for calculating the oscillatory wake solutions generated by spatially localized perturbations for one particular reaction-diiusion system, of-! type. The two methods are a semi-implicit, or implicit-explicit, nite diierence scheme based on the Crank-Nicolson algorithm, and the method of lines with Gear's method. Though both solutions ultimately converge to a common solution, the approach to this nal solution is very diierent in the two cases. The results provide a clear illustration of the care required in numerical solution of oscillatory reaction-diiusion equations.

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تاریخ انتشار 1997