The role of preconditioning in the solution of evolutionary partial differential equations by implicit Fourier pseudospectral methods

Abstract This paper examines the role of preconditioning in the solution of time-dependent partial differential equations by implicit Fourier pseudospectral methods. Both diffusive and dispersive systems are considered and it is shown in the linear analyses that preconditioning techniques can substantially improve the convergence properties of iterative methods. Computational results indicate that a similar improvement can also be achieved in the solution of model nonlinear problems. This paper also provides clarification on the use of a “staggered grid” technique for dispersive problems. The technique has been outlined in the literature, but not applied to dispersive equations.