Numerical verifications of solutions for elliptic equations with strong nonlinearity

Mitsuhiro Nakao, Nobito Yamamoto

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

Numerical methods for automatic proof of the existence and the local uniqueness of weak solutions of elliptic boundary value problems with strongly nonlinear terms are proposed. They are based on the infinite dimensional fixed point theorems and the explicit error estimates for finite element approximations. We present detailed verification procedures and numerical examples for the typical model problem: — ∆u=eu.

Original languageEnglish
Pages (from-to)535-543
Number of pages9
JournalNumerical Functional Analysis and Optimization
Volume12
Issue number5-6
DOIs
Publication statusPublished - 1991 Jan 1
Externally publishedYes

ASJC Scopus subject areas

  • Analysis
  • Signal Processing
  • Computer Science Applications
  • Control and Optimization

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