Commun. Comput. Phys., 5 (2009), pp. 350-375.


Composite Laguerre-Legendre Pseudospectral Method for Exterior Problems

Tian-Jun Wang 1, Ben-Yu Guo 2*

1 Department of Mathematics and physics, Henan University of Science and Technology, LuoYang 471003, China.
2 Department of Mathematics, Shanghai Normal University, Shanghai, 200234, China; Division of Computational Science of E-Institute of Shanghai Universities, China; and Scientific Computing Key Laboratory of Shanghai Universities, China.

Received 1 November 2007; Accepted (in revised version) 14 January 2008
Available online 1 August 2008

Abstract

In this paper, we propose a composite Laguerre-Legendre pseudospectral method for exterior problems with a square obstacle. Some results on the composite Laguerre-Legendre interpolation, which is a set of piecewise mixed interpolations coupled with domain decomposition, are established. As examples of applications, the composite pseudospectral schemes are provided for two model problems. The convergence of proposed schemes are proved. Efficient algorithms are implemented. Numerical results demonstrate the spectral accuracy in space of this new approach.

AMS subject classifications: 65M70, 41A30, 35J25, 35K20

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Key words: Composite Laguerre-Legendre interpolation, pseudospectral method for exterior problems.

*Corresponding author.
Email: byguo@shnu.edu.cn (B.-Y. Guo)
 

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