Optimal Error Estimates of the Chebyshev-Legendre Spectral Method for Solving the Generalized Burgers Equation

In this paper the Chebyshev--Legendre collocation method is applied to the generalized Burgers equation. Optimal error estimate of the method is proved for the problem with the Dirichlet boundary conditions. Also, a Legendre--Galerkin--Chebyshev collocation method is given for the generalized Burgers equation. The scheme is basically formulated in the Legendre spectral form but with the nonlinear term being treated by the Chebyshev collocation method so that the scheme can be implemented at Chebyshev--Gauss--Lobatto points efficiently. Optimal order convergence is also obtained through coupling estimates in the L2 -norm and the H1 -norm.

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