The Legendre Galerkin-Chebyshev collocation method for Burgers-like equations

A Legendre Galerkin–Chebyshev collocation method for Burgers-likeequations is developed. This method is based on the Legendre–Galerkinvariational form, but the nonlinear term and the right-handterm are treated by Chebyshev–Gauss interpolation. Errorestimates of the semi-discrete scheme and the fully discretescheme are given in the L²-norm. Numerical results indicatethat our method is as stable and accurate as the standard Legendrecollocation method, and as efficient and easy to implement asthe standard Chebyshev collocation method.