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.
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)
