Computer assisted proofs of bifurcating solutions for nonlinear heat convection problems

Mitsuhiro T. Nakao, Yoshitaka Watanabe, Nobito Yamamoto, Takaaki Nishida, Myoung Nyoung Kim

    研究成果: Contribution to journalArticle査読

    4 被引用数 (Scopus)

    抄録

    In previous works (Nakao et al., Reliab. Comput., 9(5):359-372, 2003; Watanabe et al., J. Math. Fluid Mech., 6(1):1-20, 2004), the authors considered the numerical verification method of solutions for two-dimensional heat convection problems known as Rayleigh-Bénard problem. In the present paper, to make the arguments self-contained, we first summarize these results including the basic formulation of the problem with numerical examples. Next, we will give a method to verify the bifurcation point itself, which should be an important information to clarify the global bifurcation structure, and show a numerical example. Finally, an extension to the three dimensional case will be described.

    本文言語英語
    ページ(範囲)388-401
    ページ数14
    ジャーナルJournal of Scientific Computing
    43
    3
    DOI
    出版ステータス出版済み - 6 2010

    All Science Journal Classification (ASJC) codes

    • ソフトウェア
    • 理論的コンピュータサイエンス
    • 数値解析
    • 工学(全般)
    • 計算理論と計算数学
    • 計算数学
    • 応用数学

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