A numerical verification method for nonlinear functional equations based on infinite-dimensional Newton-like iteration

Yoshitaka Watanabe, Mitsuhiro T. Nakao

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

This paper describes a numerical verification of solutions for infinite-dimensional functional equations based on residual forms and Newton-like iteration. The method is based upon a verification method previously developed by the authors. Several computer-assisted proofs for differential equations, including nonlinear partial differential equations, are presented.

Original languageEnglish
Pages (from-to)239-251
Number of pages13
JournalApplied Mathematics and Computation
Volume276
DOIs
Publication statusPublished - 2016 Mar 5
Externally publishedYes

Keywords

  • Differential equation
  • Functional equation
  • Newton-like iteration
  • Residual form

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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