具有高精度大稳定域的二阶导数方法及其stiff稳定性

STIFFLY STABLE PROPERTIES OF SECOND DERIVATIVE MULTISTEP METHODS WITH HIGHER ORDER AND IMPROVED STABILITY REGIONS

1974年Enright^1提出并构造了一类含二阶导数项的k步k+2阶stiff稳定的多步方法。之后,一些作者在增大稳定域及提高精确度方面做了一些有益的工作。本文将对这类方法作一系统研究,在建立一些理论结果的同时,构造了一类k步2k+1阶或k步2k阶的stiff稳定的二阶导数方法,这些方法的稳定域比同阶的Enright方法大,从而更为适合于求解stiff方程。

Enright proposed and constructed a class of stiffly stable second derivative multistep methods with k-step(k+2)nd order in 1974. After that, some authors worked on improving accuracy and stability regions. This paper studies this class of methods systematically, develops some theoretical results and offers a class of stiffly stable second derivative multistep methods with k-step(2k+1)nd or (2k)nd order. These new methods possess far larger regions of absolute stability and higher order than that of Enright's and they suggest their use especially for solving initial value problems of a system of stiff ordinary differential equations.