Long time integration for initial value problems of ordinary differential equations using power series arithmetic

T. Miyata*, Y. Nagatomo, M. Kashiwagi

*この研究の対応する著者

研究成果: Article査読

抄録

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.

本文言語English
ページ(範囲)2230-2237
ページ数8
ジャーナルIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
E84-A
9
出版ステータスPublished - 2001 9月

ASJC Scopus subject areas

  • 信号処理
  • コンピュータ グラフィックスおよびコンピュータ支援設計
  • 電子工学および電気工学
  • 応用数学

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