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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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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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.

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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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