求解相同PDE不同边值问题的一种简化D-N交替法  

A SIMPLIFIED D-N ALTERNATIVE METHOD FOR THE SAME PDE WITH DIFFERENT BOUNDARY CONDITIONS

作　　者：董永新[1] 王寿城[1] 

机构地区：[1]合肥工业大学数学学院,合肥230009

出　　处：《数值计算与计算机应用》2014年第2期125-130,共6页Journal on Numerical Methods and Computer Applications

摘　　要：本文构造了一种简化的D-N交替法来求解Poisson方程带有不同边值问题。先求两个方程系数矩阵,函数值差额的先验估计矩阵,再用简化的D-N交替法求解。本文的算法简化了,而且可以同时求解不同的边值问题,从而提高计算效率。文中还得出与Richardson迭代法具有最优特性等价的松弛因子θ_n以及简化D-N交替法对应问题的真解u的表达式。In this paper, we constructed a simplified D-N alternative method to solve Poisson equation with different boundary value problems. First we compute two equation＇s coefficient matrixes and the function value＇s difference preestimate matrix. Then the simplified D-N alternative method was used. The method was simplified and could solve Poisson equation with different boundary value problems once. Hence the computing efficiency was promoted. Also we got the representation of the relaxation parameter 0n which was equivalent to that in the Richardson＇s iteration, being optimal, and the true solution which was in simplified D-N alternative method of related problems u.

关 键 词：不同边值问题 POISSON方程 简化的D-N交替法 Richardson迭代 

分 类 号：O241.82[理学—计算数学]