对含二阶导数的Enright方法的改进

IMPROVEMENT ON ENRIGHT'S SECOND DERIVATIVE METHOD

本文改进了含二阶导数的Enright的四阶二步法,得到不含高阶导数的A-稳定的四阶二步法,使其用Newton迭代法来实现该方法时,会自动不出现含形为■的项.

In this paper, we point out that the conclusion as A-stable of multistep method by Enright W H in 1974 as A-stableis incorrect. By using Lemma by Sun G in 1985, the implicit two-step method of order four with A-stabilty and higher order without derivatives are suggested. When we solve it by using Newton's iteration scheme, the term as form is not appeared automatically. Thus the scheme is an improvement on W. H. Enright's second derivative method with k=2, When nonlinear order of f(x,y) with respect to y is higher, the method in this paper is also suitable for the approximate numerical integration of stiff system of frist ODE.S.