2011 Fiscal Year Final Research Report
Development of computer assisted analysis for complicated nonlinear phenomena
| Project/Area Number |
20224001
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| Research Category |
Grant-in-Aid for Scientific Research (S)
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| Allocation Type | Single-year Grants |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Sasebo National College of Technology (2010-2011)
Kyushu University (2008-2009) |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
EI Shin-ichiro 九州大学, マス・フォア・インダストリ研究所, 教授 (30201362)
TABATA Masahisa 早稲田大学, 理工学術院, 教授 (30093272)
NAGATOU Kaori 九州大学, マス・フォア・インダストリ研究所, 准教授 (40326426)
MURASHIGE Sunao 公立はこだて未来大学, システム情報科学部, 教授 (40302749)
YAMAMOTO Nobito 電気通信大学, 電気通信学部, 教授 (30210545)
WATANABE Yoshitaka 九州大学, 情報基盤研究開発センター, 准教授 (90243972)
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| Co-Investigator(Renkei-kenkyūsha) |
OISHI Shinichi 早稲田大学, 理工学術院, 教授 (20139512)
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| Project Period (FY) |
2008 – 2011
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| Keywords | 数値解析 / 精度保証付き数値計算法 / 解の数値的検証 / 解の事後誤差評価 / 計算機援用証明 / 非線形現象 / 有限要素法 |
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| Research Abstract |
We were working on the development and applications of the numerical verification methods for solutions of nonlinear partial differential equations, in particular, we succeeded in finding a new and very efficient verification principle for nonlinear evolutional problems. Also we extended and improved the existing verification methods for solutions of elliptic problems as well as we proved the effectiveness of the computer assisted proofs by applying our methods to resolve the actual nonlinear problems for which any theoretical approaches seem to be not useful to apply.
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