Abstract: 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 efect Besed on singular perturbed theory and Greens function, we have established the difference scheme that is suited for the solution to the problems. We introduce an idea of feasitbe equidistant degree a here. And this proves that if a≥2 the scheme converges in norm with speed O(h+\t) uniformly.

Key words: boundary layer, Green’s function, feasible equidistant degree, uniform convergence