# American Institute of Mathematical Sciences

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

 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.
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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