关于奇异摄动问题数值解法的一个猜测的证明

On a Conjecture for Numerical Solutions of Singular Perturbation Problems

在这篇文章中,我们就二阶常微分方程奇异摄动边值问题证明了Doolan,Miller和Schilders提出的一个猜测,即差分格式的一致收敛阶数不超过退化差分格式对退化问题的收敛阶数。对一般的线性奇异摄动问题,本文的证明方法都适用。

Doolan, Miller and Schilders in[1] put fotward a conjecture that the uniformly convergent order of a difference scheme for a singularly perturbed problem is not bigger than the convergent order of the reduced difference scheme to the reduced problem. In the paper, the conjecture is proved for nonselfadjoint and selfadjoint second order ordinary differential equations. For more general linear problems, our proving method may be applied.