Does error control suppress spuriosity?

M.A. Aves, D.F. Griffiths, D.J. Higham

Research output: Contribution to journalArticle

13 Citations (Scopus)

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 pages22
JournalSIAM Journal on Numerical Analysis
Volume34
Issue number2
DOIs
Publication statusPublished - 1997

Keywords

  • dynamics
  • long-term behavior
  • error control
  • spurious fixed point
  • mathematics

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