1998 Fiscal Year Final Research Report Summary
Qualtative Theory and Numerical Analysis on Functional Differential Eqmations
| Project/Area Number |
09640172
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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 |
解析学
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| Research Institution | Yamanashi University |
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Principal Investigator |
KURIHARA Mitsunobu Yamanashi Univ.Facul.Engineering, Professor, 工学部, 教授 (50027372)
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| Co-Investigator(Kenkyū-buntansha) |
SUZUKI Tomohiro Yamanashi Univ.Facul.of Engineering, Assistant, 工学部, 助手 (70235977)
SATO Masahisa Yamanashi Univ.Facul.of Engineering, Professor, 工学部, 教授 (30143952)
MIYAMOTO Izumi Yamanashi Univ.Facul.of Engineering, Professor, 工学部, 教授 (60126654)
SUZUKI Toshio Yamanashi Univ.Facul.of L.A.& Education, Professor, 教育人間科学部, 教授 (20020472)
NAKAI Yoshinobu Yamanashi Univ. Facul.of L.A.& Education, Professor, 教育人間科学部, 教授 (40022652)
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| Project Period (FY) |
1997 – 1998
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| Keywords | Differential Difference Equations / Boundary Value Problems / Chebyshev Polynomials / Galerkin's Procedures / Chebyshev Series / Existence Theorems / Uniform Norms |
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| Research Abstract |
We studied a boundary value problem of differential difference equations with many time lags in a real domain. A numerical process of constructing approximate solutions of was obtained by the method of Galerkin's procedure based 03 Chebysher polynomials.
Moreover an existence theorem was proved for our boudary value probrem. It said that one could always assure the existence of a Unique exact solution in the meighborhood of the obtaind approximate solutions by checking several conditions on them. Further it gave a method to obtain the error bounds of the approximate solutions. We also proved that for an isolated solution there existed an approximate solution accurately in the sense of uniform norm as it was desired by computing finite Chebysher series.
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