An enhanced pseudospectral Chebyshev method for dissipative partial differential equations

We present an enhanced pseudospectral Chebyshev method based on a postprocess previously introduced for the Galerkin method (De Frutos et al., Applied Mathematics and Computation Reports, July 1996). When the regularity of the solution is limited the new method is shown to possess a superior rate of convergence and improved efficiency than the classical pseudospectral scheme. In the particular case of smooth solutions the reduction of the error obtained by postprocessing is not so clear. However, the use of a filter in the numerical solution before applying the postprocess improves again the efficiency of the method. The numerical analysis of the new method and some numerical experiments showing its superior efficiency are presented.