A numerical approach to the proof of existence of solutions for elliptic problems II

Mitsuhiro T. Nakao

研究成果: Article査読

25 被引用数 (Scopus)

抄録

This paper is a continuation of the preceding study ([2]) in which we described an automatic proof by computer, utilizing Schauder's fixed point theorem, of the existence of weak solutions for Dirichlet problems of second order. We newly formulate a verification method using the Newton-like method and Sadovskii's fixed point theorem for the codensing map. This approach enables us to remove the magnitude limit of the spectral radius of operator appeared in the previous work. We show some numerical examples which confirm us that the method is really applicable to problems having large spectral radius.

本文言語English
ページ(範囲)477-488
ページ数12
ジャーナルJapan Journal of Applied Mathematics
7
3
DOI
出版ステータスPublished - 1990 10
外部発表はい

ASJC Scopus subject areas

  • Engineering(all)
  • Applied Mathematics

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