关于耦合型对流-扩散方程组的奇异摄动边值问题

本文考虑下述耦合型对流-扩散方程组的奇异摄动边值问题:本文提出两种方法:一种是初值化解法,用这种方法,原始问题转化成一系列没有扰动的一阶微分方程或方程组的初值问题,从而得到一个渐近展开式;第二种是边值化解法,用这种方法,原始问题转化成一组没有边界层现象的边值问题,从而可以得到精确解和使用经典的数值方法去得到具有关于摄动参数ε一致的高精度数值解.

On Singular Perturbation Boundary-Value Problem of Coupling Type System of Convection- Diffusion Equations

In this paper we consider the singular perturbation boundary-value problem of the following coupling type system of convection-diffusion equations We advance two methods: the first one is the initial value solving method, by which the original boundary-value problem is changed into a series of unperturbed initial-value problems of the first order ordinary differential equation or system so that an asymptotic expansion is obtained;the second one is the boundary-value solving method, by which the original problem is changed into a few boundary-value problems having no phenomenon of boundary-layer so that the exact solution can be obtained and any classical numerical methods can be used to obtain the numerical solution ofconsismethods can be used to obtain the numerical solution of consistant high accuracy with respect to the perturbation parameter ε.