| Presentation | 2003/12/11 Long Time Integration for IVPs of ODEs Using Affine Arithmetic Takatomi MIYATA, Masahide KASHIWAGI, |
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| PDF Download Page | PDF download Page Link |
| Abstract(in Japanese) | (See Japanese page) |
| Abstract(in English) | In this report, 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. Up to now, a lot of methods have been proposed to solve IVPs of ODES With guaranteed accuracy. Lohner's method [1] is one of the most famous method in all these methods. We also proposed a method for this problem [2]. However, we can see that the width of the inclusion may not reduce but explode in due time, by using these methods, because of the wrapping effect. On the other hand, we are also concerned with Affine Arithmetic (AA). AA is a hopeful variant of interval arithmetic (IA) proposed by Stolfi et al. [3] [4]. AA keeps correlation between quantities, so AA overcomes the essential weak points of IA. That is, AA is never affected by the wrapping effect. Our new method is the method to solve IVPs of ODES With guaranteed accuracy using AA. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | ODE / IVP / numerical method with guaranteed accuracy / wrapping effect / Affine Arithmetic |
| Paper # | NLP2003-128 |
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| Conference Information | |
| Committee | NLP |
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| Conference Date | 2003/12/11(1days) |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | |
| Topics (in Japanese) | (See Japanese page) |
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| Paper Information | |
| Registration To | Nonlinear Problems (NLP) |
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| Language | JPN |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | Long Time Integration for IVPs of ODEs Using Affine Arithmetic |
| Sub Title (in English) | |
| Keyword(1) | ODE |
| Keyword(2) | IVP |
| Keyword(3) | numerical method with guaranteed accuracy |
| Keyword(4) | wrapping effect |
| Keyword(5) | Affine Arithmetic |
| 1st Author's Name | Takatomi MIYATA |
| 1st Author's Affiliation | Faculty of Engineering, Kanazawa Institute of Technology() |
| 2nd Author's Name | Masahide KASHIWAGI |
| 2nd Author's Affiliation | School of Science and Engineering, Waseda University |
| Date | 2003/12/11 |
| Paper # | NLP2003-128 |
| Volume (vol) | vol.103 |
| Number (no) | 503 |
| Page | pp.pp.- |
| #Pages | 6 |
| Date of Issue | |