K步K阶线性多步公式集及几乎A稳定的线性多步公式

THE SET OF k-STEP ORDER k LINEAR MULTISTEP FORMULAS AND NEARLY A-STABLE LINEAR MULTISTEP FORMULAS

本文构造了K步K阶线性多步公式集.在建立一些理论结果的同时,借助于电子计算机得到了一类几乎A稳定的线性多步方法,这些方法的不稳定区域的边界在复左半平面内几乎贴近于虚轴.同时,本文也给出了显式线性多步方法的某些结果.

The set of k-step order k linear multistep formulas is constructed in this paper. Some theoretical results are given and by means of computer a class of nearly A-stable linear multistep formulas is obtained. In the complex left half plan, the regions of instability of these formulas are close to the imaginary axis. Moreobver, this paper offers some results about explicit linear multistep formulas.