Spectral and finite difference solutions of the Burgers equation

Spectral methods (Fourier Galerkin, Fourier pseudospectral, Chebyshev Tau, Chebyshev collocation, spectral element) and standard finite differences are applied to solve the Burgers equation with small viscosity (v = 1100π). This equation admits a (nonsingular) thin internal layer that must be resolved if accurate numerical solutions are to be obtained. From the reported computations, it appears that spectral schemes offer the best accuracy, especially if coordinate transformation or elemental subdivision is used to resolve the regions of large variation of the dependent variable.