一类带小参数的二维反应扩散型方程组的数值方法

The Numerical Method for System of Reaction-Diffusion Equations with a Small Parameter in Two Dimensions

本文讨论了一类带小参数的二维反应扩散型方程组的数值方法.基于奇摄动理论、Green函数、分裂方法和半群理论,建立这种类型方程组的计算格式.在误差分析中,运用了不等距步长的可行等距度,并将Lorenz的技巧用于估计解的性态.最后,得到了不等距解按l_1Ω模意义下以O(h+l十△t)的速度一致收敛.

This paper is concerned with the numerical method for system of reaction-diffusion equations in two dimensions with a small parameter. Based on singlar perturbed theory, Green's function, Splitting method and Senigroup theory the difference scheme is established. In error analysis, we use the feasible equidistant degree. We also adopt the anologous technique of [6] to obtain the estimations of the behaviour of the solution. At last, we get that the scheme convergent in l1 (Ω) norm with speed O (h +l+△l)uniformly.