Poisson方程差分格式迭代解法中一些最优参数的有理拟合方法(英文)  

The Rational Fitting Method for Determining the Optimal Parameters of Iterative Methods in Finite Difference Discretization to Poisson's Equations

作　　者：王同科[1] 曹靖[2] 

机构地区：[1]天津师范大学数学科学学院,天津300387 [2]天津理工大学数学系,天津300191

出　　处：《应用数学》2010年第2期419-425,共7页Mathematica Applicata

摘　　要：本文针对二维Poisson方程五点和九点差分格式,导出了求解这些格式的SOR方法中最优松弛因子与区域剖分数的有理拟合公式,给出了Jacobi结合Chebyshev加速方法中Jacobi迭代矩阵谱半径的有理拟合公式.实际计算表明这些公式计算效果良好.This paper presents some rational fitting formulas for determining the optimum relaxation factor of successive overrelaxation iteration method for five-point and nine-point finite difference schemes to two dimensional Poisson＇s equation.The rational fitting formulas of spectral radius of Jacobi iteration matrix are also presented for Jacobi combining with Chebyshev acceleration method.Practical computations show these formulas have very high computational efficiency.

关 键 词：二维Poisson方程 有限差分格式 最优松弛因子 有理拟合公式 

分 类 号：O241.82[理学—计算数学]