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.
| Identifer | oai:union.ndltd.org:NSYSU/oai:NSYSU:etd-0720109-211230 |
| Date | 20 July 2009 |
| Creators | Yen, Hong-da |
| Contributors | Lih-jier Young, Zi-Cai Li, Chien-Sen Huang, Tzon-Tzer Lu, Hung-Tsai Huang |
| Publisher | NSYSU |
| Source Sets | NSYSU Electronic Thesis and Dissertation Archive |
| Language | English |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0720109-211230 |
| Rights | unrestricted, Copyright information available at source archive |
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