Proposal of a new method to enginearing systems by means of ultradiscrete analysis
| Project/Area Number |
16K05048
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Computational science
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| Research Institution | Musashino University |
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Principal Investigator |
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| Project Period (FY) |
2016-10-21 – 2019-03-31
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| Project Status |
Completed (Fiscal Year 2018)
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| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2018: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2017: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2016: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Keywords | 応用数学 / 数理工学 / セルオートマトン / 非線形差分方程式 / 超離散系 / カルマンフィルター / 超離散解析 / 差分方程式 / 超離散 / 非線形方程式 |
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| Outline of Final Research Achievements |
We found several new aspects of the solutions and mathematical structures for ultradiscrete (both of the independent and dependent variables are discrete), and related discrete equations. We also studied the relationship between the solutions of ultradiscrete equations and those of the corresponding nonlinear differential equations, and made clear that both are closely related. We also proposed a Kalman filter for the ultradiscrete system corresponding to a nonlinear difference equation and confirmed its validity through numerical experiment. This result strongly suggests an applicability of the ultradiscrete equations to engineering systems. Furthermore, we propose a new type of nonlocal nonlinear difference equation, which is a model of traffic flow and can give a new insight on the relation between discrete and ultradiscrete systems.
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| Academic Significance and Societal Importance of the Research Achievements |
本研究で主な対象とした超離散的手法はコンピュータによる解析に適したもので、従来の連続解析では得られない結果も出てくることが予想される。本研究の成果が生かされて、超離散解析が新しい解析の一手法となることを強く期待している。
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Report
(4 results)
Research Products
(18 results)
