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

T. Miyata, Y. Nagatomo, Masahide 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

    Fingerprint

    Initial value problems
    Time Integration
    Power series
    Ordinary differential equations
    Initial Value Problem
    Ordinary differential equation
    First order differential equation
    Mean Value
    Normal Form
    Error Bounds
    Numerical methods
    Inclusion
    Numerical Methods
    Curve

    Keywords

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

    ASJC Scopus subject areas

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

    Cite this

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