Proposal of a new method to enginearing systems by means of ultradiscrete analysis

2018 Fiscal Year Final Research Report

• Project/Area Number: 16K05048
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Computational science
• Research Institution: Musashino University
• Principal Investigator: SATSUMA Junkichi 武蔵野大学, 工学部, 教授 (70093242)
• Project Period (FY): 2016-10-21 – 2019-03-31
• 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

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.

Free Research Field

工学、応用数理、数理物理学

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。