Abstract
A Legendre Galerkin–Chebyshev collocation method for Burgers‐like equations is developed. This method is based on the Legendre–Galerkin variational form, but the nonlinear term and the right‐hand term are treated by Chebyshev–Gauss interpolation. Error estimates of the semi‐discrete scheme and the fully discrete scheme are given in the L2‐norm. Numerical results indicate that our method is as stable and accurate as the standard Legendre collocation method, and as efficient and easy to implement as the standard Chebyshev collocation method.
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