Numerical verification of existence and inclusion of solutions for nonlinear operator equations

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

Nonlinear operator equations of the type f(u) ≡ Lu + Nu = 0, u ∈ D(L) are considered, where L is a closed linear operator from a Banach space X to another Banach space Y and N a nonlinear operator from X to Y. A method is presented for numerical verification and inclusion of solutions for the equations. As an example, the existence of a periodic solution is proved for the Duffing equation.

Original languageEnglish
Pages (from-to)171-185
Number of pages15
JournalJournal of Computational and Applied Mathematics
Volume60
Issue number1-2
DOIs
Publication statusPublished - 1995 Jun 20

Keywords

  • Computer-assisted existence proof
  • Duffing's equation
  • Newton's method
  • Self-validating numerics
  • Urabe-Galerkin's method

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Numerical verification of existence and inclusion of solutions for nonlinear operator equations'. Together they form a unique fingerprint.

  • Cite this