Ws. Don et D. Gottlieb, THE CHEBYSHEV LEGENDRE METHOD - IMPLEMENTING LEGENDRE METHODS ON CHEBYSHEV POINTS, SIAM journal on numerical analysis, 31(6), 1994, pp. 1519-1534
A new collocation method for the numerical solution of partial differe
ntial equations is presented. This method uses the Chebyshev collocati
on points, but, because of the way the boundary conditions are impleme
nted, it has all the advantages of the Legendre methods. In particular
L2 estimates can be easily obtained for hyperbolic and parabolic prob
lems.