使用迭代法的终止检验

STOPPING TEST OF ITERATIVE METHODS FOR SOLVING PDE

为了保证使用迭代法解偏微分方程数值解时的精度,终止检验是一个非常重要的问题。当线性代数方程组的系数矩阵是严格对角优势或不可约弱对角优势时,本文给出了使用迭代法u^(s+1)=Gu^(s)+K解偏微分方程时的终止检验公式。并且还给出一些数值例子。

In order to assure the accuracy of the numerical solution of the iterative method for solving PDE, the stopping test is very important.If the coefficient matrix of the system of linear algebraic equations is strictly diagonal dominant or irreducible weakly diagonal dominant, the stopping test formulas of the iterative method x(s+1)=Gx(s)+K for solving PDE is proposed in this paper. Several numerical examples are given to illustrate the applications of the stopping test formulas.