Computer assisted proofs of bifurcating solutions for nonlinear heat convection problems

Mitsuhiro T. Nakao, Yoshitaka Watanabe, Nobito Yamamoto, Takaaki Nishida, Myoung Nyoung Kim

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

In previous works (Nakao et al., Reliab. Comput., 9(5):359-372, 2003; Watanabe et al., J. Math. Fluid Mech., 6(1):1-20, 2004), the authors considered the numerical verification method of solutions for two-dimensional heat convection problems known as Rayleigh-Bénard problem. In the present paper, to make the arguments self-contained, we first summarize these results including the basic formulation of the problem with numerical examples. Next, we will give a method to verify the bifurcation point itself, which should be an important information to clarify the global bifurcation structure, and show a numerical example. Finally, an extension to the three dimensional case will be described.

Original languageEnglish
Pages (from-to)388-401
Number of pages14
JournalJournal of Scientific Computing
Volume43
Issue number3
DOIs
Publication statusPublished - Jun 1 2010

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All Science Journal Classification (ASJC) codes

  • Software
  • Theoretical Computer Science
  • Numerical Analysis
  • Engineering(all)
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics

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