Stiff微分方程初值问题的一类数值方法

1.引言 实践表明,数值积分常微分方程初值问题 dx/dt=f(t,x), (1.1) x(t_0)=x_0时,若(1.1)是Stiff的,积分过程的稳定性是一个突出的问题.用传统的数值方法,比如Euler法,Adams法或Runge-Kutta法,为了保证计算稳定,积分步长受到相当地限制.即使运算速度为 100万次/秒的计算机,计算时间也将成为重大的负担.

A FAMILY OF NUMERICAL METHODS FOR THE SOLUTION OF INITIAL VALUE PROBLEM OF STIFF DIFFERENTIAL EQUATIONS

In this paper, a family of numerical methods with stable parameter for thesolution of Stiff Differential Equations is derived. Each method in the family can be foundfrom a general formula by choosing a value for the parameter S Which is Called stable para-meter. A simple relation between the parameter S and the region of absolute stability is studied.When S = 0, this family of numerical methods is simply either classical Adams or Runge-Kutta method. We can choose parameter S to improve absolute stability, i. e. to extend theregion of absolute stability.