Pseudospectral method using generalizedLaguerre functions for singular problems on unbounded domains

Zhong-Qing Wang; Ben-Yu Guo; Yan-Na Wu

doi:10.3934/dcdsb.2009.11.1019

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2009, Volume 11, Issue 4: 1019-1038. Doi: 10.3934/dcdsb.2009.11.1019

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

1.
Department of Mathematics, Shanghai Normal University, Shanghai, 200234
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: November 2009

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Abstract

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.

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Mathematics Subject Classification: Primary: 65N35, 41A05, 33C45, 35J70.

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