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: Article査読

5 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English
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Published - 2010 6月
外部発表はい

ASJC Scopus subject areas

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

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