The effect of filtering on the pseudospectral solution of evolutionary partial differential equations

Abstract This paper examines the effect of filtering on the solution of time-dependent partial differential equations by the pseudospectral method. It is shown that if spatial discretisation is effected using the Fourier pseudospectral method the computed solution will be an approximation to the solution of a modified differential equation. The changes in dispersive and dissipative properties induced by the modification are examined, and numerical results are presented which illustrate these changes for both linear and nonlinear equations. Numerical results are also presented which show the effect of filtering on Chebyshev pseudospectral solutions of time-dependent equations.