一类含有稳定参数的Adams型隐式方法及其新算法

§1.引言 数值积分Stiff常微分方程初值问题,其积分过程的稳定性相当重要.用传统的数值方法,如Adams方法等,为保证计算稳定性,积分步长受到相当的限制.在stiff常微分方程初值问题的数值解法中,Gear方法是目前最通用的方法之一.但是,当阶p大

A CLASS OF ADAMS IMPLICIT METHODS WITH STABLE PARAMETER AND A NEW ALGORITHM

In this paper, a class of Adams implicit methods, principally of order three and order four,with stable parameter s are derived for the solution of stiff equations. The parameter s can beappropriately chosen so as to improve absolute stability, i.e. to extend arbitrarily the region ofabsolute stability, and to assure zero-stability. A new iteration algorithm is given for the me-thods. Lastly, some numerical examples are provided to show that not only do this class ofmethods have better stability and precision, but the convergence rate of the new iteration schemeis faster than the original scheme.