Composite Legendre–Laguerre pseudospectral approximation in unbounded domains

A composite Legendre-Laguerre pseudospectral approximation in unbounded domains is developed. Some approximation results are obtained. As an application, a composite pseudospectral scheme is proposed for the Burgers equation on the half-line. The stability and convergence of the scheme are proved. By choosing appropriate base functions, the resulting system of this method has a sparse structure and can be solved in parallel. Numerical results are given to show the efficiency of this new method.