解常微分方程初值问题的K步k+1阶线性多步公式集及其stiff稳定性

SET OF K-STEP ORDER k+1 LINEAR MULTISEP FORMULAS AND STIFF STABIITY FOR SOLVING INITIAL VALUE PROBLEMS IN ODE'S

本文利用算子方法导出了一般的k步k+1阶线性多步公式集其中的系数β_i及误差系数C_(k+2)可以表示为α_i的函数(i=0,1,2,…,k):从而可以方便地构造出满足稳定性要求的任意k步k+1阶线性多步公式,并同时给出它的误差系数。是否存在k步k+1阶stiff稳定的线性多步公式?,对于k=1,2,3的情形,本文作出了论证,答案是否定的。

In this paper, by means of operator notation we have developed the general k-step order k+1 linear multistep formulas where, the coefficients β_i and error coefficient Ck+2 can be expressed as functions of a_i: Therefore, we can conveniently form any k-step order k+l stable linear multistep formulas and obtain its error coefficients. Do there exist k-step order k+1 stiffly stable linear multistep formulas? Fork=1, 2, 3a demonstration is offered in the paper. The answers is negative.