Chebyshev rational spectral and pseudospectral methods on a semi-infinite interval

A weighted orthogonal system on the half-line based on the Chebyshev rational functions is introduced. Basic results on Chebyshev rational approximations of several orthogonal projections and interpolations are established. To illustrate the potential of the Chebyshev rational spectral method, a model problem is considered both theoretically and numerically: error estimates for the Chebyshev rational spectral and pseudospectral methods are established; preliminary numerical results agree well with the theoretical estimates and demonstrate the effectiveness of this approach. Copyright (C) 2001 John Wiley & Sons, Ltd.