解含转向点问题的完全指数型拟合差分方法

本文对含转向点的微分方程边值问题建立了完全指数型拟合差分格式,证明了此格式具有一阶一致收敛性.推广了Miller[1]的方法,简化了证明过程.数值结果表明本格式比Il'in[2]格式要好.

Completely Exponentially Fitted Finite Difference Methods for Problems of Turning Point

In this paper we construct a completely exponentially fitted finite difference scheme for the boundary value problem of differential equation with turning points, extending Miller's method[1] and simplifying the method of the proof. We prove the first order uniform convergence of the scheme. The numerical results show that it is better than Il'in's scheme.