An efficient estimate based on FFT in topological verification method

Yasuaki Hiraoka, Toshiyuki Ogawa

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


In this paper, localized patterns of the quintic Swift-Hohenberg equation are studied. A numerical verification method with the Conley index theory developed in Zgliczyński and Mischaikow [Rigorous numerics for partial differential equations: the Kuramoto-Sivashinsky equation, Found. Comput. Math. 1 (2001) 255-288] is used in order to prove these patterns. A new technique to efficiently obtain estimates for nonlinear terms is presented. The key idea is based on the pseudo-spectral method. It is shown that this technique is inevitable for the verification of the localized patterns.

Original languageEnglish
Pages (from-to)238-244
Number of pages7
JournalJournal of Computational and Applied Mathematics
Issue number2
Publication statusPublished - 2007 Feb 15


  • Conley index
  • FFT
  • Numerical verification

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics


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