The Chebyshev-Legendre method: implementing Legendre methods on Chebyshev points

A new collocation method for the numerical solution of partial differential equations is presented. This method uses the Chebyshev collocation points, but, because of the way the boundary conditions are implemented, it has all the advantages of the Legendre methods. In particular $L_2 $ estimates can be easily obtained for hyperbolic and parabolic problems.