Storner-Cowell: straight, summed and split; An overview

J.F. Frankena

    Research output: Contribution to journalArticleAcademicpeer-review

    2 Citations (Scopus)
    54 Downloads (Pure)

    Abstract

    In this paper we consider the relationship between some (forms of) specific numerical methods for (second-order) initial value problems. In particular, the Störmer-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 Störmer-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.
    Original languageEnglish
    Pages (from-to)129-154
    Number of pages26
    JournalJournal of computational and applied mathematics
    Volume62
    Issue number2
    DOIs
    Publication statusPublished - 1995

    Keywords

    • Ordinary differential equations
    • Periodic solutions
    • Summed forms
    • Split forms
    • Numerical methods
    • Multistep methods
    • Initial value problems

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