Composite Legendre-Laguerre pseudospectral approximation in unbounded domains (Q2725340)

The authors propose a pseudospectral method on a half line. The basis consists of Legendre polynomials on a finite subinterval and Laguerre functions on the rest of the domain. The method is applied to Burgers' equation with a rather large diffusion coefficient. The resulting method of lines is shown to be stable. The suggested time discretization is explicit in the advection term and implicit in the diffusion term.