Pseudospectral method using generalizedLaguerre functions for singular problems on unbounded domains

Abstract

In this paper, we develop a pseudospectral method for differentialequations defined on unbounded domains. We first introduceGauss-type interpolations using a family of generalized Laguerrefunctions, and establish basic approximation results. Then wepropose a pseudospectral method for differential equations onunbounded domains, whose coefficients may degenerate or grow up. Asexamples, we consider two model problems. The proposed schemes matchthe underlying problems properly and exhibit spectral accuracy. Numerical results demonstrate the efficiency of this new approach.