A numerical verification of nontrivial solutions for the heat convection problem

Yoshitaka Watanabe*, Nobito Yamamoto, Mitsuhiro T. Nakao, Takaaki Nishida

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

19 Citations (Scopus)


A computer assisted proof of the existence of nontrivial steady-state solutions for the two-dimensional Rayleigh-Bénard convection is described. The method is based on an infinite dimensional fixed-point theorem using a Newton-like operator. This paper also proposes a numerical verification algorithm which generates automatically on a computer a set. including the exact nontrivial solution. All discussed numerical examples take into account of the effects of rounding errors in the floating point computations.

Original languageEnglish
Pages (from-to)1-20
Number of pages20
JournalJournal of Mathematical Fluid Mechanics
Issue number1
Publication statusPublished - 2004
Externally publishedYes


  • Computer assisted proof
  • Fixed-point theorem
  • Rayleigh-Bénard convection

ASJC Scopus subject areas

  • Mathematical Physics
  • Condensed Matter Physics
  • Computational Mathematics
  • Applied Mathematics


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