Volume 1, Issue 3
Mixed Fourier-Jacobi Spectral Method for Two-Dimensional Neumann Boundary Value Problems

East Asian J. Appl. Math., 1 (2011), pp. 284-296.

Published online: 2018-02

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• 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.

• Keywords

Mixed Fourier-Jacobi orthogonal approximation spectral method Neumann boundary value problem

33C45 65M70 35J25

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@Article{EAJAM-1-284, author = {Xu-Hong Yu and Zhong-Qing Wang}, title = {Mixed Fourier-Jacobi Spectral Method for Two-Dimensional Neumann Boundary Value Problems}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {1}, number = {3}, pages = {284--296}, 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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.281010.200411a}, url = {http://global-sci.org/intro/article_detail/eajam/10909.html} }
TY - JOUR T1 - Mixed Fourier-Jacobi Spectral Method for Two-Dimensional Neumann Boundary Value Problems AU - Xu-Hong Yu & Zhong-Qing Wang JO - East Asian Journal on Applied Mathematics VL - 3 SP - 284 EP - 296 PY - 2018 DA - 2018/02 SN - 1 DO - http://doi.org/10.4208/eajam.281010.200411a UR - https://global-sci.org/intro/article_detail/eajam/10909.html KW - Mixed Fourier-Jacobi orthogonal approximation KW - spectral method KW - Neumann boundary value problem AB -

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.

Xu-Hong Yu & Zhong-Qing Wang. (1970). Mixed Fourier-Jacobi Spectral Method for Two-Dimensional Neumann Boundary Value Problems. East Asian Journal on Applied Mathematics. 1 (3). 284-296. doi:10.4208/eajam.281010.200411a
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