病态线性代数方程组的一种刚性问题数值解法

1．引言文［1，2］中提出的预估校正法是国内计算数学工作者研究刚性常微分方程数值解法的较早期的工作．并且作者将自己构造的算法用于解病态线性代数方程组卜个FORTRAN标准程序见3]）．文4,5］根据李雅普诺夫稳定性理论建立了病态线性代数方程组的解与对应刚性常微分方程组初值问题的解之间的关系并且采用Lambert提出的解刚性问题的非线性单步方法问给出了解病态线性代数方程组的非线性迭代法．但这个非线性方法有两大缺点：第一，数值解不能有零分量；第二，代数精确度较差．为此本文采用局部指数逼近法建立的解刚性问题的二阶显式…

A NUMERICAL METHOD OF STIFF PROBLEMS FOR ILL-CONDITIONED LINEAR SYSTEMS OF ALGEBRAIC EQUATIONS

Basing on the relationship between ill-conditioned linear systems of algebraic equations and stiff systems of ordinary differelltial equations and using an explicit single step method with 2-order for stiff systems, the numerical solution of the initial value problems relative to the ill-conditioned linear systems of algebraic equations is obtained. So does the approkimation solution of the ill-conditioned linear systems of algebraic equations.