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

T. Miyata, Y. Nagatomo, M. Kashiwagi

Research output: Contribution to journalArticle

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.

Original languageEnglish
Pages (from-to)2230-2237
Number of pages8
JournalIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
VolumeE84-A
Issue number9
Publication statusPublished - 2001 Sep

Keywords

  • Mean value form
  • Numerical method with guaranteed accuracy
  • Ordinary differential equation
  • Power series arithmetic
  • Wrapping effect

ASJC Scopus subject areas

  • Signal Processing
  • Computer Graphics and Computer-Aided Design
  • Electrical and Electronic Engineering
  • Applied Mathematics

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