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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Computer-assisted Proof
Heat convection
Convection
Heat
Fluids
Numerical Verification
Numerical Examples
Global Bifurcation
Bifurcation Point
Rayleigh
Verify
Fluid
Three-dimensional
Formulation

All Science Journal Classification (ASJC) codes

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

Cite this

Computer assisted proofs of bifurcating solutions for nonlinear heat convection problems. / Nakao, Mitsuhiro T.; Watanabe, Yoshitaka; Yamamoto, Nobito; Nishida, Takaaki; Kim, Myoung Nyoung.

In: Journal of Scientific Computing, Vol. 43, No. 3, 01.06.2010, p. 388-401.

Research output: Contribution to journalArticle

Nakao, Mitsuhiro T. ; Watanabe, Yoshitaka ; Yamamoto, Nobito ; Nishida, Takaaki ; Kim, Myoung Nyoung. / Computer assisted proofs of bifurcating solutions for nonlinear heat convection problems. In: Journal of Scientific Computing. 2010 ; Vol. 43, No. 3. pp. 388-401.
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