A numerical verification method for the existence of weak solutions for nonlinear boundary value problems

Mitsuhiro T. Nakao*

*この研究の対応する著者

研究成果: Article査読

50 被引用数 (Scopus)

抄録

In this paper, we consider a numerical technique which enables us to verify the existence of solutions for nonlinear two point boundary value problems (BVP). We formulate the problem as a fixed point of a Newton-like operator and present a verification algorithm by computer based on Sadovskii's fixed point theorem. In order to compute the Newton type iterative sequences in infinite dimensional space, two concepts, the rounding and the rounding error, are introduced. Also some numerical examples are illustrated. We emphasize that, since the present method uses the weak formulation of BVP and the finite element approximations instead of the existing validation techniques, it is aslo applicable, in principle, to the BVP for partial differential equations as it stands.

本文言語English
ページ(範囲)489-507
ページ数19
ジャーナルJournal of Mathematical Analysis and Applications
164
2
DOI
出版ステータスPublished - 1992 3 1
外部発表はい

ASJC Scopus subject areas

  • 分析
  • 応用数学

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