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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| Project Status |
Completed (Fiscal Year 2010)
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| Budget Amount *help |
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2009: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2008: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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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 / 微分差分方程式 / 離散型病理モデル / Lotka-Volterraモデル / 固有値計算 / 離散型SIRモデル / 大域漸近安定性 / パーマネンス / 固有値 / 関数微分方程式 / 大域的安定性 |
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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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Report
(4 results)
Research Products
(25 results)
