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Spectral methods using generalized Laguerre functions for second and fourth order problems |
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| Authors: | Fu-jun Liu Hui-yuan Li Zhong-qing Wang |
| Institution: | 1.Department of Mathematics,Shanghai Normal University,Shanghai,China;2.School of Science,Henan Institute of Engineering,Zhengzhou,China;3.State Key Laboratory of Computer Science/Laboratory of Parallel Computing, Institute of Software,Chinese Academy of Sciences,Beijing,China;4.School of Science,University of Shanghai for Science and Technology,Shanghai,China |
| Abstract: | Spectral methods using generalized Laguerre functions are proposed for second-order equations under polar (resp. spherical) coordinates in ?2 (resp. ?3) and fourth-order equations on the half line. Some Fourier-like Sobolev orthogonal basis functions are constructed for our Laguerre spectral methods for elliptic problems. Optimal error estimates of the Laguerre spectral methods are obtained for both second-order and fourth-order elliptic equations. Numerical experiments demonstrate the effectiveness and the spectral accuracy. |
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