Numerical Verification Methods for Dynamical Systems described by ODEs
| Project/Area Number |
17540106
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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 | The University of Electro-Communications |
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Principal Investigator |
YAMAMOTO Nobito The University of Electro-Communications, Department of Electro-Communications, Professor (30210545)
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| Co-Investigator(Kenkyū-buntansha) |
NAKAMURA Ken-ichi UEC, Department of Electro-Communications, Assistant Professor (40293120)
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| Project Period (FY) |
2005 – 2006
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| Project Status |
Completed (Fiscal Year 2006)
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| Budget Amount *help |
¥2,700,000 (Direct Cost: ¥2,700,000)
Fiscal Year 2006: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2005: ¥1,600,000 (Direct Cost: ¥1,600,000)
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| Keywords | numerical verification method / dynamical system / ODE / non-linear system / chaos / 精度補償 |
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| Research Abstract |
The present research has two purposes.
1. Investigating self-validated computation methods which have been developed so far, we select various techniques as useful tools for study of dynamical systems.
2. We develop new theoretical scheme and techniques for improvement of self-validated computation of dynamical systems.
There are several methods for self-validated computation of initial value problems of ODEs. Among them, Lohner method and TM method are well-known, which have their theoretical base on Taylor expansion and its error estimation. The main reason which extends the error in the validated computation is so-called wrapping effect. These methods use QR factorization in order to reduce the wrapping effect. We applied this technique to the Nakao's method which has been developed for validated computation of PDEs and tried to construct a numerical verification methods for ODEs based on the Nakao's method. But we found that a straightforward application does not work well. Then we have investigated
1) Reduction of the wrapping effect in the step-wise procedure by the Nakao's method.
2) How to handle the large size matrices which appear in the whole time procedure by the Nakao's method
3) Applications of the Nakao's method on boundary value problems to ODEs in order to get narrow error bound at the end point
and obtained some results on new theoretical scheme and techniques for improvement of self-validated computation of dynamical systems
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Report
(3 results)
Research Products
(12 results)
