Asymptotic expansions using blow-up

Stephanus A. van Gils, M. Krupa, P Szmolyan

    Research output: Contribution to journalArticleAcademicpeer-review

    22 Citations (Scopus)

    Abstract

    The method of matched asymptotic expansions and geometric singular perturbation theory are the most common and successful approaches to singular perturbation problems. In this work we establish a connection between the two approaches in the context of the simple fold problem. Using the blow-up technique [5], [12] and the tools of geometric singular perturbation theory we derive asymptotic expansions of slow manifolds continued beyond the fold point. Our analysis explains the structure of the expansion and gives an algorithm for computing its coefficients.
    Original languageUndefined
    Article number10.1007/s00033-004-1021-y
    Pages (from-to)369-397
    Number of pages29
    JournalZeitschrift für angewandte Mathematik und Physik
    Volume56
    Issue number3
    DOIs
    Publication statusPublished - 12 May 2005

    Keywords

    • asymptotic expansions
    • invariant manifolds
    • Singular perturbation
    • Blow-up
    • IR-72130
    • METIS-226015
    • EWI-14018

    Cite this

    van Gils, Stephanus A. ; Krupa, M. ; Szmolyan, P. / Asymptotic expansions using blow-up. In: Zeitschrift für angewandte Mathematik und Physik. 2005 ; Vol. 56, No. 3. pp. 369-397.
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    abstract = "The method of matched asymptotic expansions and geometric singular perturbation theory are the most common and successful approaches to singular perturbation problems. In this work we establish a connection between the two approaches in the context of the simple fold problem. Using the blow-up technique [5], [12] and the tools of geometric singular perturbation theory we derive asymptotic expansions of slow manifolds continued beyond the fold point. Our analysis explains the structure of the expansion and gives an algorithm for computing its coefficients.",
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    van Gils, SA, Krupa, M & Szmolyan, P 2005, 'Asymptotic expansions using blow-up', Zeitschrift für angewandte Mathematik und Physik, vol. 56, no. 3, 10.1007/s00033-004-1021-y, pp. 369-397. https://doi.org/10.1007/s00033-004-1021-y

    Asymptotic expansions using blow-up. / van Gils, Stephanus A.; Krupa, M.; Szmolyan, P.

    In: Zeitschrift für angewandte Mathematik und Physik, Vol. 56, No. 3, 10.1007/s00033-004-1021-y, 12.05.2005, p. 369-397.

    Research output: Contribution to journalArticleAcademicpeer-review

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    AU - Krupa, M.

    AU - Szmolyan, P

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    N2 - The method of matched asymptotic expansions and geometric singular perturbation theory are the most common and successful approaches to singular perturbation problems. In this work we establish a connection between the two approaches in the context of the simple fold problem. Using the blow-up technique [5], [12] and the tools of geometric singular perturbation theory we derive asymptotic expansions of slow manifolds continued beyond the fold point. Our analysis explains the structure of the expansion and gives an algorithm for computing its coefficients.

    AB - The method of matched asymptotic expansions and geometric singular perturbation theory are the most common and successful approaches to singular perturbation problems. In this work we establish a connection between the two approaches in the context of the simple fold problem. Using the blow-up technique [5], [12] and the tools of geometric singular perturbation theory we derive asymptotic expansions of slow manifolds continued beyond the fold point. Our analysis explains the structure of the expansion and gives an algorithm for computing its coefficients.

    KW - asymptotic expansions

    KW - invariant manifolds

    KW - Singular perturbation

    KW - Blow-up

    KW - IR-72130

    KW - METIS-226015

    KW - EWI-14018

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    DO - 10.1007/s00033-004-1021-y

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