带小参数的反应—扩散方程组的数值方法

Numerical Method for the System of Reaction-Diffusion Equations with a Small Parameter

本文讨论带小参数的反应—扩散方程组的数值方法.由于边界层效应,使得这类问题的数值求解十分困难.我们根据奇异摄动理论和Green函数方法建立起一种适合求解这类问题的差分格式.在文中,我们引入了可行等距度α,并证明了若a≥2则格式在l_1(m)意义下一致收敛且收敛阶为O(h+△t).

This paper deals with the numerical method for the system of reaction-diffusion equations with a small parameter. It is difficult to solve the problems of this kind numerically because of the boundary layer effect. Based on singular perturbed theory and Green's function, we have established the difference scheme that is suited for the solution to the problems. We introduce an idea of feasible equidistant degree a here. And this proves that if α≥2, the scheme converges in l1(m) norm with speed O(h+Δt) uniformly.