2014 Fiscal Year Final Research Report
Application of Ultradiscrete Analysis on Engineering Systems
| Project/Area Number |
24560078
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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 |
Engineering fundamentals
|
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| Research Institution | Musashino University (2014)
Aoyama Gakuin University (2012-2013) |
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Principal Investigator |
|
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| Project Period (FY) |
2012-04-01 – 2015-03-31
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| Keywords | 応用数理 / 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 |
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| Outline of Final Research Achievements |
We found several new aspects of the solutions and mathematical structures for ultradiscrete equations, in which both of the independent and dependent variables are discrete. 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.
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| Free Research Field |
応用数理、数理物理学
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