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 |
| 巻 | 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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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
}
TY - JOUR
T1 - A numerical verification of nontrivial solutions for the heat convection problem
AU - Watanabe, Yoshitaka
AU - Yamamoto, Nobito
AU - Nakao, Mitsuhiro T.
AU - Nishida, Takaaki
PY - 2004/12/1
Y1 - 2004/12/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=10044237618&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=10044237618&partnerID=8YFLogxK
U2 - 10.1007/s00021-003-0077-3
DO - 10.1007/s00021-003-0077-3
M3 - Article
AN - SCOPUS:10044237618
VL - 6
SP - 1
EP - 20
JO - Journal of Mathematical Fluid Mechanics
JF - Journal of Mathematical Fluid Mechanics
SN - 1422-6928
IS - 1
ER -