Study of the properties of some difference equations and application of computation

2018 Fiscal Year Final Research Report

• Project/Area Number: 26400212
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Foundations of mathematics/Applied mathematics
• Research Institution: Tokyo University of Science
• Principal Investigator: Ishiwata Emiko 東京理科大学, 理学部第一部応用数学科, 教授 (30287958)
• Project Period (FY): 2014-04-01 – 2019-03-31
• Keywords: 時間遅れ / 差分方程式 / 数理生物モデル / 超離散化 / 安定性

Outline of Final Research Achievements

Due to the reality of mathematical models of infections, the effects of time delays are often studied recently. Proper discretization to keep the solution positive is important to understand the behavior of such a model.
We newly tried to apply these ideas to the ultra-discrete models. As a result, clear correspondence in the qualitative property was confirmed among the continuous model, the discretized model, and the ultra-discrete model including time delay.
Moreover, through the help of graduate students, we derived results such as convergence behavior for a kind of the integrable discrete hungry systems and formulation of calculation procedure of eigenpairs. Related papers have been published.

Free Research Field

数値解析

Academic Significance and Societal Importance of the Research Achievements

昨今のウィルスの感染伝播の脅威に対し，数理モデルによる解明は重要視されている。これらの時間発展による具体的な挙動の把握に差分方程式の解明は役立つと考える。