一类求解刚性常微分方程组的线性隐式Hybrid单步法

A CLASS OF LINEAR IMPLICIT HYBRID ONE-STEP METHODS FOR SOLUTION OF STIFF ODES

本文在Enright[1]二阶导数单步法的基础上引入一个非步点,并且f的全导数用几个函数值的线性组合来代替,构造了一类适合于求解刚性(Stiff)常微分方程组的Hybrid单步法。它们均是四阶收敛的,通过对参数的适当选择可使这些方法具有L——稳定性;并分别改进了Enright的二阶导数单步法和Usmani[2]、Jacques[3]的组合单步法。文末的数值例子表明,本文所构造的方法优于[1、2、3]中的同类方法。

In this paper, we proposed a class of linear implicit hybrid one-step methods suitable for the approximate numerical integration of stiff system of ODES. By judicious choice of the coefficients in these formulas, we obtained twa classes of four order L-stable methods. These methods have the advantages of higher accuracy and good stability compared with these methods in (1)-(3). Numerical results showed that these schemes proposed by this paper are quite efficient for solving somes stiff system of ODES.