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Mixed Fourier-Jacobi Spectral Method for Two-Dimensional Neumann Boundary Value Problems

Published online by Cambridge University Press:  28 May 2015

Xu-Hong Yu  and
Zhong-Qing Wang
Xu-Hong Yu
Affiliation:
Department of Mathematics, Shanghai Normal University, Shanghai, 200234, China
Zhong-Qing Wang*
Affiliation:
Scientific Computing Key Laboratory of Shanghai Universities, Division of Computational Science of E-institute ofShanghai Universities
*
Corresponding author. Email: zqwang@shnu.edu.cn
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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

33C4565M7035J25Mixed Fourier-Jacobi orthogonal approximationspectral methodNeumann boundary value problem
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 1 , Issue 3 , August 2011 , pp. 284 - 296
Copyright
Copyright © Global-Science Press 2011

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