刚性方程的数值求解法(一)
来源期刊:中南大学学报(自然科学版)1982年第1期
论文作者:乔际岳
文章页码:39 - 46
关键词:刚性方程; 数值求解; 数值计算方法; 变换矩阵; 离散化; 微分方程组; 数值法; 特征值; 阶跃函数; 正弦函数
摘 要:当关联系统矩阵 A 具有非常分散的特征值时,就会出现刚性性质。在这种情况下,要想找一个稳定的数值求解微分方程的方法是非常困难的。迄今尚无一种方法能合理地求解刚性方程。本文提出了一种特殊的方法,即仅对矩阵做一些乘方运算就能完成大量步数的数值计算。此法将能用足够微小的步长去保证计算方法的稳定与精度,因此能够解决线性刚性方程的求解问题。
Abstract:
Stiffness occurs whenever the associated system matrix A possesses widely separated eigenvalues.In this condition,it is difficult to find a numerical stable algorithem to solve differential equation.So far there has been no approach to solving the stiff equation reasonably.
In this article we have supplied a specific algorithem which,doing some squaring operations,can complete a great number of time steps in computation.Thus,this method will allow us to use sufficiently small step sizes so as to guarantee the stability and accuracy.Therefore we can solve the problem of the linear stiff differential equation.