2010 Fiscal Year Final Research Report
Stability and numerical analysis for delay differential equations
| Project/Area Number |
20540137
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Tokyo University of Science |
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Principal Investigator |
ISHIWATA Emiko Tokyo University of Science, 理学部, 准教授 (30287958)
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| Project Period (FY) |
2008 – 2010
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| Keywords | 遅延微分方程式 / 数値解析 / 大域安定性 / 数理生物モデル |
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| Research Abstract |
We obtained some results related to the functional differential equations by this grant. We first derived new global stability conditions for a class of difference equations with time delay. Next, we showed an attainable order of collocation methods for delay differential and Volterra integral equations with proportional delay. Super attainable order was also considered. Finally, we considered some global stability for epidemic models with time delay. Using a discretization of combined explicit with implicit schemes, we obtained the global dynamics of a discretized SIRS epidemic model with time delay, corresponding to that of continuous model.
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