| Presentation | 1998/3/13 A Numerical Method to Prove the Existence of Solutions for Ordinary Differential Equations Using Infinite Matrix Takatomi MIYATA, Takao SOMA, Yuchi KANZAWA, Shin'ichi OISHI, Kazuo HORIUCHI, |
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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 method for numerical verification of existence and inclusion of solutions for ordinary differential equation in case that certain approximate solution is given. It can be realized by expressing the original problem in simultaneous form of the first ordinary differential equations. We consider the infinite-dimensional vector space which consists of Fourier series coefficients of each elements of the vector valued function. In this report, we estimate the norm of the inverse of the infinite matrix instead of that of the original problem. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | Infinite Matrix / Fourier Series / Ordinary Differential Equation / Banach's Contraction Mapping Theorem |
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| Committee | NLP |
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| Conference Date | 1998/3/13(1days) |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | |
| Topics (in Japanese) | (See Japanese page) |
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| 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) | A Numerical Method to Prove the Existence of Solutions for Ordinary Differential Equations Using Infinite Matrix |
| Sub Title (in English) | |
| Keyword(1) | Infinite Matrix |
| Keyword(2) | Fourier Series |
| Keyword(3) | Ordinary Differential Equation |
| Keyword(4) | Banach's Contraction Mapping Theorem |
| 1st Author's Name | Takatomi MIYATA |
| 1st Author's Affiliation | School of Science and Engineering, Waseda University() |
| 2nd Author's Name | Takao SOMA |
| 2nd Author's Affiliation | School of Science and Engineering, Waseda University |
| 3rd Author's Name | Yuchi KANZAWA |
| 3rd Author's Affiliation | School of Science and Engineering, Waseda University |
| 4th Author's Name | Shin'ichi OISHI |
| 4th Author's Affiliation | School of Science and Engineering, Waseda University |
| 5th Author's Name | Kazuo HORIUCHI |
| 5th Author's Affiliation | School of Science and Engineering, Waseda University |
| Date | 1998/3/13 |
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| Volume (vol) | vol.97 |
| Number (no) | 592 |
| Page | pp.pp.- |
| #Pages | 6 |
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