Abstract
The pseudospectral method has under-used advantages in problems involving shocks and discontinuities. These emerge from superior accuracy in phase and group velocities as compared to finite difference schemes of all orders. Dispersion curves for finite difference schemes suggest that group velocity error typically outranks Gibbs' error as a cause of numerical oscillation. A flux conservative form of the pseudospectral method is derived for compatibility with flux limiters used to preserve monotonicity. The resulting scheme gives high quality results in linear advection and shock formation/propagation examples.
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