2001 Fiscal Year Final Research Report Summary
Numerical Methods Based on Sinc Functions
| Project/Area Number |
11450038
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Engineering fundamentals
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| Research Institution | Nagoya University |
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Principal Investigator |
SUGIURA Masaaki School of engineering, Nagoya University, Professor, 工学研究科, 教授 (80154483)
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| Co-Investigator(Kenkyū-buntansha) |
MATSUO Takayasu School of engineering, Nagoya University, Research Associate, 工学研究科, 助手 (90293670)
SUGIURA Hiroshi School of engineering, Nagoya University, Associate Professor, 工学研究科, 助教授 (60154465)
MITSUI Taketomo School of Human Informatics, Professor, 人間情報学研究科, 教授 (50027380)
OGATA Hidenori Ehime University, Faculty of Engineering, Lecturer, 工学部, 講師 (50242037)
MORI Masatake Tokyo Denki University, School of Sincence and Engineering, Professor, 理工学部, 教授 (20010936)
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| Project Period (FY) |
1999 – 2001
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| Keywords | Sinc functions / Sinc numerical methods / spectral methods / double exponential transformation / indefinite integrals / 2-point boundary value problems / Sturm-Liouville eigenvalue problems / Poisson equations |
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| Research Abstract |
This project aims at developing numerical methods based on Sine functions incorporated with the double exponential transformation technique. The following results have been obtained.
1. A Sinc method using the double exponential transformation technique is developed for computing indefinite integrals. Two Sinc methods using the conventional single exponential transformation technique are well-known : one is due to Kearfott, and the other due to Haber. While these well-known methods converge at the rate exp(-c-√<n>) (n : the number of function evaluations), our method converges at the rate exp(-c'n/ log n).
2. A Sinc-Galerkin method incorporated with the double exponential transformation technique for two-point boundary value problems is developed. While the rate of the convergence of the original Sinc-Galerkin method due to Stenger is exp(-c-√<n>)(n: the number of basis functions), that of our method is exp(-c'n/ logn), which is a remarkable improvement.
3. A Sinc-collocation method combined with the double exponential transformation technique for Sturm-Liouville eigenvalue problems is developed. Our method enjoyes the convergence rate O(exp(-c'n/ logn)) (n : the number of basis functions), whereas the original Sine-collocation method proposed by Lund et al. does the convergence rate O(exp(-c-√<n>)).
4. Three spectral methods using the double exponential transformation technique are developed for solving the Poisson equation on a fan-shaped domain. One employes the Sinc functions as basis functions, another does the Legendre polynomials, and the other does the Chebyshev polynomials. All the methods converge at the rate exp(-c√<n>/logn), where n is the number of basis functions.
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