An accurate Fourier splitting scheme for solving the cubic quintic complex Ginzburg-Landau equation

In this paper, we present a splitting scheme for the pseudo-spectral numerical method namely the Split-Step Fourier method (SSFM), in our approach we expand the exponential term in a manner that a succession of linear and nonlinear terms are distributed uniformly along one step size, the splitting will be performed symmetrically, this new scheme will be tested on one of the most used nonlinear partial deferential equation in optics, namely the cubic quintic complex Ginzburg-Landau (CQCGL) equation, in this work we demonstrate that the accuracy of the Split Step Fourier method scheme can be improved by expanding and distributing it in small parts within one step. (C) 2014 Elsevier Ltd. All rights reserved.