An efficient approach to the numerical verification for solutions of elliptic differential equations

Mitsuhiro T. Nakao, Yoshitaka Watanabe

研究成果: Article査読

18 被引用数 (Scopus)

抄録

The authors and their colleagues have developed numerical verification methods for solutions of second-order elliptic boundary value problems based on the infinite-dimensional fixed-point theorem using the Newton-like operator with appropriate approximation and constructive a priori error estimates for Poisson's equations. Many verification results show that the authors' methods are sufficiently useful when the equation has no first-order derivative. However, in the case that the equation includes the term of a first-order derivative, there is a possibility that the verification algorithm does not work even though we adopt a sufficiently accurate approximation subspace. The purpose of this paper is to propose an alternative method to overcome this difficulty. Numerical examples which confirm the effectiveness of the new method are presented.

本文言語English
ページ(範囲)311-323
ページ数13
ジャーナルNumerical Algorithms
37
1-4 SPEC. ISS.
DOI
出版ステータスPublished - 2004 12
外部発表はい

ASJC Scopus subject areas

  • 応用数学

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