弱非线性椭圆型方程的Ritz-Galerkin解法和差分解法探讨

Analysis of Ritz-Galerkin Solutions and Discrete Solutions of MildlyNonlinear Elliptic Differential Equation

本文给出了Ritz-Galerkin解法的收敛性,并对模型问题的块Jacobi和平行弦方法进行收敛性分析.Bers在1964年给出模型问题差分方法收敛性的证明,这里得到了块Jacobi块SOR、块Newton-Jacobi和块Newton-sor四种算法的收敛性结果.以上这些Jacobi算法都适合于并行计算,最后给出两个具体数值例子.

In this paper the Convergence of Ritz-Galerkin method is given,and the convergences of B-J method and parallel chord method are discussed. Bers solved the discrete method convengence of mothod problem. The convergences of B-J-M , BSOR, BNJ, BNSOR methods are obtained. All these Jacobi methods are suitable to parallel computing. In the end two numerical results are given.