二维刚性边值问题的小波-吉尔解法

本文利用微分方程数值解的离散小波表示，讨论了此类方程在满足一定初始条件和边值条件下，在一个方向上利用小波伽辽金法，另一方向上利用吉尔方法进行求解，提出了一种解二维刚性初，边值问题的小波数值算法，计算结果表明，利用该方法所求得的数值解精度高，而且由小波特有的性质，它特别适用于求解带有奇异摄动的刚性问题。

WAVELETS-GEAR SOLUTION OF TWO-DIMENSIONAL STIFF BOUNADARY PROBLEM

In this paper, we present a wavelet\|numerical algorithm for solving the two\|dimensional stiff boundary problem of partial differential equations. The algorithm makes use of the discrete wavelet representation of differential equation's numerical solution to discuss this kind of equation satisfying certain initial and boundary condition. We adapt the Wavelet Galerkin method to solve it in one direction, and in the other direction we make use of Gear method. The results indicate that the above method's accuracy is high and efficient. Furthermore, the above method, owing to special wavelet property, especially adapt to the stiff problem with the singular perturbation problem.