Generalized Laguerre Interpolation and Pseudospectral Method for Unbounded Domains

Abstract

In this paper, error estimates for generalized Laguerre--Gauss-type interpolations are derived in nonuniformly weighted Sobolev spaces weighted with $\omega_{\alpha,\beta}(x)=x^{\alpha}e^{-\beta x},\;\alpha >-1,\beta>0.$ Generalized Laguerre pseudospectral methods are analyzed and implemented. Two model problems are considered. The proposed schemes keep spectral accuracy and, with suitable choice of basis functions, lead to sparse and symmetric linear systems.