Optimal Spectral-Galerkin Methods Using Generalized Jacobi Polynomials |
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| Authors: | Ben-Yu Guo Jie Shen Li-Lian Wang |
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| Affiliation: | (1) Department of Mathematics, Shanghai Normal University and Shanghai E-Institute for Computational Sciences, Shanghai, 200234, P. R. China;(2) Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA;(3) Division of Mathematics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, 639798, Singapore |
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| Abstract: | We extend the definition of the classical Jacobi polynomials withindexes α, β>−1 to allow α and/or β to be negative integers. We show that the generalized Jacobi polynomials, with indexes corresponding to the number of boundary conditions in a given partial differential equation, are the natural basis functions for the spectral approximation of this partial differential equation. Moreover, the use of generalized Jacobi polynomials leads to much simplified analysis, more precise error estimates and well conditioned algorithms.Mathematics subject classification 1991. 65N35, 65N22, 65F05, 35J05 |
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| Keywords: | Generalized Jacobi polynomials spectral-Galerkin method high-order differential equations |
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