A method of proving the existence of simple turning points of two-point boundary value problems based on the numerical computation with guaranteed accuracy

Takao Soma, ShiN'ichi Oishi, Yuchi Kanzawa, Kazuo Horiuchi

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

This paper is concerned with the validation of simple turning points of two-point boundary value problems of nonlinear ordinary differential equations. Usually it is hard to validate approximate solutions of turning points numerically because of it's singularity. In this paper, it is pointed out that applying the infinite dimensional Krawcyzk-based interval validation method to enlarged system, the existence of simple turning points can be verified. Taking an example, the result of validation is also presented.

Original languageEnglish
Pages (from-to)1892-1897
Number of pages6
JournalIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
VolumeE81-A
Issue number9
Publication statusPublished - 1998
Externally publishedYes

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Boundary value problems
Ordinary differential equations

Keywords

  • Enlarged systems
  • Krawczyk's mapping
  • Numerical computation with guaranteed accuracy
  • Turning points
  • Two-point boundary-value problems

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Hardware and Architecture
  • Information Systems

Cite this

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AU - Kanzawa, Yuchi

AU - Horiuchi, Kazuo

PY - 1998

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AB - This paper is concerned with the validation of simple turning points of two-point boundary value problems of nonlinear ordinary differential equations. Usually it is hard to validate approximate solutions of turning points numerically because of it's singularity. In this paper, it is pointed out that applying the infinite dimensional Krawcyzk-based interval validation method to enlarged system, the existence of simple turning points can be verified. Taking an example, the result of validation is also presented.

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