| URN |
etd-0720109-211230 |
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| Author |
Hong-da Yen |
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| Author's Email Address |
No Public. |
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| Statistics |
This thesis had been viewed 5582 times. Download 1499 times. |
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| Department |
Applied Mathematics |
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| Year |
2008 |
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| Semester |
2 |
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| Degree |
Master |
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| Type of Document |
|
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| Language |
English |
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| Title |
On the Increasingly Flat RBFs Based Solution Methods for Elliptic PDEs and Interpolations |
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| Date of Defense |
2009-06-04 |
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| Page Count |
70 |
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| Keyword |
multiquadric collocation method
meshless method
error estimate
arbitrary precision computation
RBF Limit
Spectral Collocation Method using Polynomial
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| Abstract |
Many types of radial basis functions, such as multiquadrics, contain a free parameter called shape factor, which controls the flatness of RBFs. In the 1-D problems, Fornberg et al. [2] proved that with simple conditions on the increasingly flat radial basis function, the solutions converge to the Lagrange interpolating. In this report, we study and extend it to the 1-D Poisson equation RBFs direct solver, and observed that the interpolants converge to the Spectral Collocation Method using Polynomial. In 2-D, however, Fornberg et al. [2] observed that limit of interpolants fails to exist in cases of highly regular grid layouts. We also test this in the PDEs solver and found the error behavior is different from interpolating problem. |
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| Advisory Committee |
Zi-Cai Li - chair
Tzon-Tzer Lu - co-chair
Lih-jier Young - co-chair
Hung-Tsai Huang - co-chair
Chien-Sen Huang - advisor
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| Files |
indicate access worldwide |
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| Date of Submission |
2009-07-20 |
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