Numerical verification of solutions of parametrized nonlinear boundary value problems with turning points

Takuya Tsuchiya, Mitsuhiro T. Nakao

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

Nonlinear boundary value problems (NBVPs in abbreviation) with parameters are called parametrized nonlinear boundary value problems. This paper studies numerical verification of solutions of parametrized NBVPs defined on one-dimensional bounded intervals. Around turning points the original problem is extended so that the extended problem has an invertible Fréchet derivative. Then, the usual procedure of numerical verification of solutions can be applied to the extended problem. A numerical example is given.

Original languageEnglish
Pages (from-to)357-372
Number of pages16
JournalJapan Journal of Industrial and Applied Mathematics
Volume14
Issue number3
DOIs
Publication statusPublished - 1997
Externally publishedYes

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Keywords

  • Numerical verification of solutions
  • Parametrized nonlinear boundary value problems
  • Regular branches
  • Turning points

ASJC Scopus subject areas

  • Engineering(all)
  • Applied Mathematics

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