| Project/Area Number |
16K05270
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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 |
Foundations of mathematics/Applied mathematics
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| Research Institution | Iwate University |
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Principal Investigator |
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| Project Period (FY) |
2016-04-01 – 2022-03-31
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| Project Status |
Completed (Fiscal Year 2021)
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| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2020: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2019: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2018: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2017: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 遅延微分方程式 / 非線形固有値問題 / 精度保証付き数値計算 / 精度保証付き数値計算法 |
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| Outline of Final Research Achievements |
In general, results of numerical computations do not coincide with exact solutions, since some kinds of errors are included. In order to obtain exact conclusions from the numerical results, we need to estimate the errors and compute intervals enclosing the exact solutions. Numerical verification algorithms have been developed for this purpose.
In this study, we established a numerical verification algorithm for solution to nonlinear eigenvalue problems arising from delay differential equation. Moreover, we established numerical verification algorithms for matrix equations and functions by exploiting the idea obtained during the development of the algorithms for solution to nonlinear eigenvalue problems.
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| Academic Significance and Societal Importance of the Research Achievements |
遅延微分方程式はは制御理論, 生物学, 交通モデリング, ニューラルネットワーク, 機械学, 電子回路等, 科学技術の分野に広く現れる. 多くの応用において, 安定な解が要求される．本研究で確立した手法により，この方程式の解の安定性について，理論的に厳密かつ極めて正確な結論を計算機により得ることが可能となる．
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