Does error control suppress spuriosity?

Mark A. Aves, David Griffiths, Desmond. J. Higham

    Research output: Contribution to journalArticlepeer-review

    13 Citations (Scopus)
    200 Downloads (Pure)

    Abstract

    In the numerical solution of initial value ordinary differential equations, to what extent does local error control confer global properties? This work concentrates on global steady states or fixed points. It is shown that, for systems of equations, spurious fixed points generally cease to exist when local error control is used. For scalar problems, on the other hand, locally adaptive algorithms generally avoid spurious fixed points by an indirect method|the stepsize selection process causes spurious fixed points to be unstable. However, problem classes exist where, for arbitrarily small tolerances, stable spurious fixed points persist with significant basins of attraction. A technique is derived for generating such examples.
    Original languageEnglish
    Pages (from-to)756-778
    Number of pages23
    JournalSIAM Journal on Numerical Analysis
    Volume34
    Issue number2
    DOIs
    Publication statusPublished - Apr 1997

    Keywords

    • Dynamics
    • Long-term behavior
    • Error control
    • Spurious fixed point

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