IEICE TRANSACTIONS on Fundamentals
A Method of Proving the Existence of Simple Turning Points of Two-Point Boundary Value Problems Based on the Numerical Computation with Guaranteed Accuracy
Summary :
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.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E81-A No.9 pp.1892-1897
- Publication Date
- 1998/09/25
- Publicized
- Online ISSN
- DOI
- Type of Manuscript
- Special Section PAPER (Special Section on Nonlinear Theory and Its Applications)
- Category
- Numerical Analysis
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Takao SOMA, Shin'ichi OISHI, Yuchi KANZAWA, Kazuo HORIUCHI, "A Method of Proving the Existence of Simple Turning Points of Two-Point Boundary Value Problems Based on the Numerical Computation with Guaranteed Accuracy" in IEICE TRANSACTIONS on Fundamentals,
vol. E81-A, no. 9, pp. 1892-1897, September 1998, doi: .
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.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e81-a_9_1892/_p
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@ARTICLE{e81-a_9_1892,
author={Takao SOMA, Shin'ichi OISHI, Yuchi KANZAWA, Kazuo HORIUCHI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={A Method of Proving the Existence of Simple Turning Points of Two-Point Boundary Value Problems Based on the Numerical Computation with Guaranteed Accuracy},
year={1998},
volume={E81-A},
number={9},
pages={1892-1897},
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.},
keywords={},
doi={},
ISSN={},
month={September},}
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TY - JOUR
TI - A Method of Proving the Existence of Simple Turning Points of Two-Point Boundary Value Problems Based on the Numerical Computation with Guaranteed Accuracy
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1892
EP - 1897
AU - Takao SOMA
AU - Shin'ichi OISHI
AU - Yuchi KANZAWA
AU - Kazuo HORIUCHI
PY - 1998
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E81-A
IS - 9
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - September 1998
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.
ER -
English
