A numerical verification of nontrivial solutions for the heat convection problem

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

    研究成果: Contribution to journalArticle査読

    17 被引用数 (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.

    本文言語英語
    ページ(範囲)1-20
    ページ数20
    ジャーナルJournal of Mathematical Fluid Mechanics
    6
    1
    DOI
    出版ステータス出版済み - 12 1 2004

    All Science Journal Classification (ASJC) codes

    • 数理物理学
    • 凝縮系物理学
    • 計算数学
    • 応用数学

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