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Efficient Chebyshev Spectral Method for Solving Linear Elliptic PDEs Using Quasi-Inverse Technique

Published online by Cambridge University Press:  28 May 2015

Fei Liu ,
Xingde Ye  and
Xinghua Wang
Fei Liu*
Affiliation:
Department of Mathematics, Zhejiang University, Hangzhou, Zhejiang 310027, China
Xingde Ye*
Affiliation:
Department of Mathematics, Zhejiang University, Hangzhou, Zhejiang 310027, China
Xinghua Wang*
Affiliation:
Department of Mathematics, Zhejiang University, Hangzhou, Zhejiang 310027, China
*
Corresponding author.Email address:liufei84@gmail.com
Corresponding author.Email address:xingdeye@zju.edu.cn
Corresponding author.Email address:xinghua@familywang.net
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Abstract

We present a systematic and efficient Chebyshev spectral method using quasi-inverse technique to directly solve the second order equation with the homogeneous Robin boundary conditions and the fourth order equation with the first and second boundary conditions. The key to the efficiency of the method is to multiply quasi-inverse matrix on both sides of discrete systems, which leads to band structure systems. We can obtain high order accuracy with less computational cost. For multi-dimensional and more complicated linear elliptic PDEs, the advantage of this methodology is obvious. Numerical results indicate that the spectral accuracy is achieved and the proposed method is very efficient for 2-D high order problems.

Keywords

65N3565N2265F0535J05Chebyshev spectral methodquasi-inverseHelmholtz equationRobin boundary conditionsgeneral biharmonic equation
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 4 , Issue 2 , May 2011 , pp. 197 - 215
Copyright
Copyright © Global Science Press Limited 2011

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