小参数常微分方程守恒型差分格式的一致收敛性

本文考虑自共轭常微分方程奇异摄动边值问题,构造一族带拟合因子的差分格式,给出差分格式解一致收敛于微分方程解的充分条件,由此提出几个具体格式,在条件较弱的情况下,给出较高的一致收敛阶。

Uniform Convergence for the Difference Scheme in the Conservation Form of Ordinary Differential Equation with a Small Parameter

In this paper, we consider a singular perturbation boundary problem for a self-adjoint ordinary differential equaiton. We construct a class of difference schemes with fitted factors, and give the sufficient conditions under which the solution of difference scheme converges uniformly to the solution of differential equation. From this we propose several specific schemes under weaker conditions, and give much higher order of uniform convergence.