椭圆-抛物偏微分方程奇异摄动问题的差分解法

本文讨论了含有小参数在高阶导数项的椭圆型方程奇异摄动问题的差分解法.当ε=0时椭圆型方程退化为抛物型方程.作者根据此问题解的边界层性质,构造了特殊的差分格式:研究了它的收敛性和解的渐近性态.最后给出一个数值例题.

The Difference Method for the Solution of Singular-Perturbation Problems for the Elliptic-Parabolic Partial Differential Equation

In this paper is discussed the difference method for the solution of singular perturbation problems for the elliptic equations,involving small parameter in the higher derivatives,As ε=0,the original equations are degenerated into the parabalic equations.Authors constructed special difference scheme by means of the boundary layer properties of the solutions of these problems and investigated the convergence of this scheme and asymptotic behaviour of the solutions,Finally,a numerical example is given.