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East Asian Journal on Applied Mathematics, 1 (2011), pp. 284-296. |
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Mixed Fourier-Jacobi Spectral Method for Two-Dimensional Neumann Boundary Value Problems Xu-Hong Yu 1, Zhong-Qing Wang 1* 1 Department of Mathematics, Shanghai Normal University, Shanghai, 200234, China. Scientific Computing Key Laboratory of Shanghai Universities, Division of Computational Science of E-institute of Shanghai Universities.Received 28 October 2010; Accepted (in revised version) 20 April 2011 Available online 27 July 2011 doi:10.4208/eajam.281010.200411a Abstract In this paper, we propose a mixed Fourier-Jacobi spectral method for two dimensional Neumann boundary value problem. This method differs from the classical spectral method. The homogeneous Neumann boundary condition is satisfied exactly. Moreover, a tridiagonal matrix is employed, instead of the full stiffness matrix encountered in the classical variational formulation. For analyzing the numerical error, we establish the mixed Fourier-Jacobi orthogonal approximation. The convergence of proposed scheme is proved. Numerical results demonstrate the efficiency of this approach. AMS subject classifications: 33C45, 65M70, 35J25 Key words: Mixed Fourier-Jacobi orthogonal approximation, spectral method, Neumann boundary value problem. *Corresponding author. Email: zqwang@shnu.edu.cn (Z. Wang) |