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

T. Miyata, Y. Nagatomo, Masahide Kashiwagi

研究成果: Article

### 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.

元の言語 English 2230-2237 8 IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E84-A 9 Published - 2001 9

### 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

### ASJC Scopus subject areas

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

### これを引用

：: IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, 巻 E84-A, 番号 9, 09.2001, p. 2230-2237.

研究成果: Article

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AU - Nagatomo, Y.

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