Studies on verified numerical computations for nonlinear parabolic partial differential equations
| Project/Area Number |
15K17596
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Foundations of mathematics/Applied mathematics
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| Research Institution | University of Tsukuba (2016-2017)
Waseda University (2015) |
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Principal Investigator |
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| Research Collaborator |
OISHI SHIN'ICHI 早稲田大学, 理工学術院, 教授
KUBO TAKAYUKI 筑波大学, 数理物質系, 講師
MATSUE KANAME 九州大学, マス・フォア・インダストリ研究所, 助教
MIZUGUCHI MAKOTO 早稲田大学, 理工学術院, 次席研究員
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| Project Period (FY) |
2015-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | 精度保証付き数値計算 / 非線形放物型偏微分方程式 / 解の数値的検証 / 爆発問題 / ケラー・シーゲル方程式系 / 非線形発展方程式 / 数値解析 |
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| Outline of Final Research Achievements |
Partial differential equations (PDEs), which expresses some relations using derivatives of unknown functions, frequently occur when natural phenomena in the world are modeled as mathematical problems. In the field of natural science, it is a subject of research to solve such PDEs mathematically or numerically to specify the unknown function. In this study, we have developed a computer-assisted method to numerically verify the existence/non-existence of solutions to nonlinear parabolic PDEs, which appear in the combustion theory of solid fuel and in the mathematical model of biological growth. Such a method validates whether the exact solution exists in the neighborhood of a numerically computed approximate solution. This is called verified numerical computations and is gaining attention as a modern approach to mathematical analysis of differential equations.
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Report
(4 results)
Research Products
(49 results)
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[Presentation] Verified numerical computations for blow-up solutions of ODEs2016
Author(s)
Akitoshi Takayasu, Kaname Matsue, Takiko Sasaki, Kazuaki Tanaka, Makoto Mizuguchi, Shin'ichi Oishi
Organizer
the 17th International Symposium on Scientific Computing, Computer Arithmetics and Verified Numerics (SCAN 2016)
Place of Presentation
Uppsala, Sweden
Year and Date
2016-09-26
Related Report
Int'l Joint Research
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[Presentation] 間違える数値計算とその対策2016
Author(s)
高安亮紀
Organizer
第144回リスク工学研究会（RERM）
Place of Presentation
筑波大学 筑波キャンパス（茨城県つくば市）
Year and Date
2016-05-16
Related Report
Invited
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