Aves, M.A. and Griffiths, D.F. and Higham, D.J. (1997) *Does error control suppress spuriosity?* SIAM Journal on Numerical Analysis, 34 (2). pp. 756-778. ISSN 0036-1429

## 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.

Item type: | Article |
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ID code: | 188 |

Keywords: | dynamics, long-term behavior, error control, spurious fixed point, mathematics, Mathematics, Numerical Analysis |

Subjects: | Science > Mathematics |

Department: | Faculty of Science > Mathematics and Statistics |

Related URLs: | |

Depositing user: | Ms Sarah Scott |

Date Deposited: | 02 Mar 2006 |

Last modified: | 04 Sep 2014 09:57 |

URI: | http://strathprints.strath.ac.uk/id/eprint/188 |

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