Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Invariant curves for numerical methods

Author: H. T. Doan
Journal: Quart. Appl. Math. 43 (1985), 385-393
MSC: Primary 65L05; Secondary 58F99
DOI: https://doi.org/10.1090/qam/814235
MathSciNet review: 814235
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Abstract: The problem of finding periodic orbits of dynamical systems numerically is considered. It is shown that if a convergent, strongly stable, multi-step method is employed then under some suitable conditions, there exist invariant curves. The result also shows that the rates of convergence toward the invariant curves are roughly the same for different methods and different step sizes.

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DOI: https://doi.org/10.1090/qam/814235
Article copyright: © Copyright 1985 American Mathematical Society

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