A numerical verification of nontrivial solutions for the heat convection problem

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

研究成果: ジャーナルへの寄稿記事

16 引用 (Scopus)

抄録

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.

元の言語英語
ページ(範囲)1-20
ページ数20
ジャーナルJournal of Mathematical Fluid Mechanics
6
発行部数1
DOI
出版物ステータス出版済み - 12 1 2004

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Computer-assisted Proof
Numerical Verification
Heat convection
Rounding error
Floating point
Steady-state Solution
Nontrivial Solution
Rayleigh
Convection
Fixed point theorem
convection
Heat
heat
Numerical Examples
Operator
newton
floating
theorems
operators

All Science Journal Classification (ASJC) codes

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

これを引用

A numerical verification of nontrivial solutions for the heat convection problem. / Watanabe, Yoshitaka; Yamamoto, Nobito; Nakao, Mitsuhiro T.; Nishida, Takaaki.

:: Journal of Mathematical Fluid Mechanics, 巻 6, 番号 1, 01.12.2004, p. 1-20.

研究成果: ジャーナルへの寄稿記事

Watanabe, Yoshitaka ; Yamamoto, Nobito ; Nakao, Mitsuhiro T. ; Nishida, Takaaki. / A numerical verification of nontrivial solutions for the heat convection problem. :: Journal of Mathematical Fluid Mechanics. 2004 ; 巻 6, 番号 1. pp. 1-20.
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