STORMER-COWELL - STRAIGHT, SUMMED AND SPLIT - AN OVERVIEW

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:62

Article

FRANKENA, JF

关键词: ORDINARY DIFFERENTIAL EQUATIONS;    PERIODIC SOLUTIONS;    INITIAL VALUE PROBLEMS;    NUMERICAL METHODS;    MULTISTEP METHODS;    SUMMED FORMS;    SPLIT FORMS;   

DOI  :  10.1016/0377-0427(94)00102-0

来源: Elsevier

【 摘 要 】

In this paper we consider the relationship between some (forms of) specific numerical methods for (second-order) initial value problems. In particular, the Stormer-Cowell method in second-sum form is shown to be the Gauss-Jackson method (and analogously, for the sake of completeness, we relate Adams-Bashforth-Moulton methods to their first-sum forms). Furthermore, we consider the split form of the Stormer-Cowell method. The reason for this consideration is the fact that these summed and split forms exhibit a better behaviour with respect to rounding errors than the original method (whether in difference or in ordinate notation). Numerical evidence will support the formal proofs that have been given elsewhere.

【 授权许可】

Free