Abstract

The spectral methods offer very high spatial resolution for a wide range of nonlinear wave equations so for the best computational efficiency it should be desirable to use also high order methods in time but without very strict restrictions on the step size by reason of numerical stability In this paper we study the exponential time differencing fourthorder Runge Kutta ETDRK4 method this scheme was derived by Cox and Matthews in S M Cox P C Matthews Exponential time differencing for stiff systems J Comp Phys 176 2002 430 455 and was modified by Kassam and Trefethen in A Kassam L N Trefethen Fourth-order time stepping for stiff PDEs SIAM J Sci Comp 26 2005 1214 1233 We compute its amplification factor and plot its stability region which gives us an explanation of its good behavior for dissipative and dispersive problems We apply this method to the Kuramoto-Sivashinsky Equation obtaining excellent results