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

Mitsuhiro T. Nakao

Research output: Contribution to journalArticle

24 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)477-488
Number of pages12
JournalJapan Journal of Applied Mathematics
Volume7
Issue number3
DOIs
Publication statusPublished - 1990 Oct
Externally publishedYes

Fingerprint

Spectral Radius
Elliptic Problems
Existence of Solutions
Newton-like Method
Schauder Fixed Point Theorem
Existence of Weak Solutions
Dirichlet Problem
Continuation
Fixed point theorem
Numerical Examples
Operator

Keywords

  • boundary value problems
  • error estimates
  • finite element method
  • fixed point theorem

ASJC Scopus subject areas

  • Engineering(all)
  • Applied Mathematics

Cite this

A numerical approach to the proof of existence of solutions for elliptic problems II. / Nakao, Mitsuhiro T.

In: Japan Journal of Applied Mathematics, Vol. 7, No. 3, 10.1990, p. 477-488.

Research output: Contribution to journalArticle

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