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June  2009, 11(4): 1019-1038. doi: 10.3934/dcdsb.2009.11.1019

Pseudospectral method using generalized Laguerre functions for singular problems on unbounded domains

Zhong-Qing Wang 1, , Ben-Yu Guo 2, and  Yan-Na Wu 1,

1. 

Department of Mathematics, Shanghai Normal University, Shanghai, 200234, China, China
2. 

Department of Mathematics, Shanghai Normal University, Shanghai 200234, Scientific Computing Key Laboratory of Shanghai Universities, Shanghai E-institute for Computational Science

Received  March 2008 Revised  February 2009 Published  April 2009

In this paper, we develop a pseudospectral method for differential equations defined on unbounded domains. We first introduce Gauss-type interpolations using a family of generalized Laguerre functions, and establish basic approximation results. Then we propose a pseudospectral method for differential equations on unbounded domains, whose coefficients may degenerate or grow up. As examples, we consider two model problems. The proposed schemes match the underlying problems properly and exhibit spectral accuracy. Numerical results demonstrate the efficiency of this new approach.
Keywords: exterior problems., Gauss-type interpolations using generalized Laguerre functions, pseudospectral method for singular differential equations on unbounded domains.
Mathematics Subject Classification: Primary: 65N35, 41A05, 33C45, 35J7.
Citation: Zhong-Qing Wang, Ben-Yu Guo, Yan-Na Wu. Pseudospectral method using generalized Laguerre functions for singular problems on unbounded domains. Discrete and Continuous Dynamical Systems - B, 2009, 11 (4) : 1019-1038. doi: 10.3934/dcdsb.2009.11.1019
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