IEICE TRANSACTIONS on Fundamentals
Long Time Integration for Initial Value Problems of Ordinary Differential Equations Using Power Series Arithmetic
Summary :
In this paper, we present a numerical method with guaranteed accuracy to solve initial value problems (IVPs) of normal form simultaneous first order ordinary differential equations (ODEs) which have wide domain. Our method is based on the algorithm proposed by Kashiwagi, by which we can obtain inclusions of exact values at several discrete points of the solution curve of ODEs. The method can be regarded as an extension of the Lohner's method. But the algorithm is not efficient for equations which have wide domain, because the error bounds become too wide from a practical point of view. Our purpose is to produce tight bounds even for such equations. We realize it by combining Kashiwagi's algorithm with the mean value form. We also consider the wrapping effects to obtain tighter bounds.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E84-A No.9 pp.2230-2237
- Publication Date
- 2001/09/01
- Publicized
- Online ISSN
- DOI
- Type of Manuscript
- Special Section PAPER (Special Section on Nonlinear Theory and its Applications)
- Category
- Numerical Method & Optimization
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Takatomi MIYATA, Yasutaka NAGATOMO, Masahide KASHIWAGI, "Long Time Integration for Initial Value Problems of Ordinary Differential Equations Using Power Series Arithmetic" in IEICE TRANSACTIONS on Fundamentals,
vol. E84-A, no. 9, pp. 2230-2237, September 2001, doi: .
Abstract: In this paper, we present a numerical method with guaranteed accuracy to solve initial value problems (IVPs) of normal form simultaneous first order ordinary differential equations (ODEs) which have wide domain. Our method is based on the algorithm proposed by Kashiwagi, by which we can obtain inclusions of exact values at several discrete points of the solution curve of ODEs. The method can be regarded as an extension of the Lohner's method. But the algorithm is not efficient for equations which have wide domain, because the error bounds become too wide from a practical point of view. Our purpose is to produce tight bounds even for such equations. We realize it by combining Kashiwagi's algorithm with the mean value form. We also consider the wrapping effects to obtain tighter bounds.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e84-a_9_2230/_p
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@ARTICLE{e84-a_9_2230,
author={Takatomi MIYATA, Yasutaka NAGATOMO, Masahide KASHIWAGI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Long Time Integration for Initial Value Problems of Ordinary Differential Equations Using Power Series Arithmetic},
year={2001},
volume={E84-A},
number={9},
pages={2230-2237},
abstract={In this paper, we present a numerical method with guaranteed accuracy to solve initial value problems (IVPs) of normal form simultaneous first order ordinary differential equations (ODEs) which have wide domain. Our method is based on the algorithm proposed by Kashiwagi, by which we can obtain inclusions of exact values at several discrete points of the solution curve of ODEs. The method can be regarded as an extension of the Lohner's method. But the algorithm is not efficient for equations which have wide domain, because the error bounds become too wide from a practical point of view. Our purpose is to produce tight bounds even for such equations. We realize it by combining Kashiwagi's algorithm with the mean value form. We also consider the wrapping effects to obtain tighter bounds.},
keywords={},
doi={},
ISSN={},
month={September},}
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TY - JOUR
TI - Long Time Integration for Initial Value Problems of Ordinary Differential Equations Using Power Series Arithmetic
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2230
EP - 2237
AU - Takatomi MIYATA
AU - Yasutaka NAGATOMO
AU - Masahide KASHIWAGI
PY - 2001
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E84-A
IS - 9
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - September 2001
AB - In this paper, we present a numerical method with guaranteed accuracy to solve initial value problems (IVPs) of normal form simultaneous first order ordinary differential equations (ODEs) which have wide domain. Our method is based on the algorithm proposed by Kashiwagi, by which we can obtain inclusions of exact values at several discrete points of the solution curve of ODEs. The method can be regarded as an extension of the Lohner's method. But the algorithm is not efficient for equations which have wide domain, because the error bounds become too wide from a practical point of view. Our purpose is to produce tight bounds even for such equations. We realize it by combining Kashiwagi's algorithm with the mean value form. We also consider the wrapping effects to obtain tighter bounds.
ER -
English
