抄録
A computer-assisted proof of non-trivial steady-state solutions for the Kolmogorov flows is described. The method is based on the infinite-dimensional fixed-point theorem using Newton-like operator. This paper also proposes a numerical verification algorithm which generates automatically on a computer a set including the exact non-trivial solution with local uniqueness. All discussed numerical results take into account the effects of rounding errors in the floating point computations.
| 元の言語 | 英語 |
|---|---|
| ページ（範囲） | 953-966 |
| ページ数 | 14 |
| ジャーナル | Journal of Computational and Applied Mathematics |
| 巻 | 223 |
| 発行部数 | 2 |
| DOI | |
| 出版物ステータス | 出版済み - 1 15 2009 |
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All Science Journal Classification (ASJC) codes
- Computational Mathematics
- Applied Mathematics
これを引用
A computer-assisted proof for the Kolmogorov flows of incompressible viscous fluid. / Watanabe, Yoshitaka.
：: Journal of Computational and Applied Mathematics, 巻 223, 番号 2, 15.01.2009, p. 953-966.研究成果: ジャーナルへの寄稿 › 記事
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TY - JOUR
T1 - A computer-assisted proof for the Kolmogorov flows of incompressible viscous fluid
AU - Watanabe, Yoshitaka
PY - 2009/1/15
Y1 - 2009/1/15
N2 - A computer-assisted proof of non-trivial steady-state solutions for the Kolmogorov flows is described. The method is based on the infinite-dimensional fixed-point theorem using Newton-like operator. This paper also proposes a numerical verification algorithm which generates automatically on a computer a set including the exact non-trivial solution with local uniqueness. All discussed numerical results take into account the effects of rounding errors in the floating point computations.
AB - A computer-assisted proof of non-trivial steady-state solutions for the Kolmogorov flows is described. The method is based on the infinite-dimensional fixed-point theorem using Newton-like operator. This paper also proposes a numerical verification algorithm which generates automatically on a computer a set including the exact non-trivial solution with local uniqueness. All discussed numerical results take into account the effects of rounding errors in the floating point computations.
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UR - http://www.scopus.com/inward/citedby.url?scp=56949087917&partnerID=8YFLogxK
U2 - 10.1016/j.cam.2008.03.034
DO - 10.1016/j.cam.2008.03.034
M3 - Article
AN - SCOPUS:56949087917
VL - 223
SP - 953
EP - 966
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
SN - 0377-0427
IS - 2
ER -