具奇解问题的Shortley-Weller逼近:收敛性与数值计算(英文)  

Shortley-Weller approximation for problems with singular solutions:convergence and numerical computation

作　　者：伍渝江[1] 吴永庆[2] 

机构地区：[1]兰州大学数学与统计学院,兰州730000 [2]辽宁工程技术大学基础教学部,辽宁葫芦岛125105

出　　处：《应用数学与计算数学学报》2013年第1期16-32,共17页Communication on Applied Mathematics and Computation

基　　金：supported by the National Basic Research Program of China(973 Program)(2011CB706903);the Natural Science Foundation of Gansu Province(3ZS041-A25-011)

摘　　要：介绍求解方形区域上具无界导数的一类二阶椭圆方程的Shortley-Weller有限差分逼近的收敛性与数值计算,考虑拟一致网格而保证了相应的矩阵为M矩阵.进一步证明了采用适当的坐标变换可加速近似解收敛,且最优加速效果取决于所考虑椭圆方程的系数取值.数值结果证实了所作分析.The convergence analysis and numerical experiments of a Shortley- Weller finite difference approximation are presented for solving a class of second- order elliptic equations with unbounded derivatives on a square domain. Quasiuniform meshes are used to ensure the resulted matrix to be an M-matrix. Fur- thermore, it is shown that the convergence of the approximate solution can be accelerated by a suitable coordinate transformation, and the optimal effect of the acceleration depends on the coefficients of the underlining elliptic equations. Nu- merical results for an example are also included to confirm the analysis.

关 键 词：Shortley-Weller逼近 二阶椭圆方程 拟一致网格 加速技巧 

分 类 号：O241.82[理学—计算数学]