Three-Step Predictor-Corrector of Exponential Fitting Method for NonlinearSchrodinger Equations

We develop the three-step explicit and implicit schemes of exponential fitting methods. We use the threet-step explicit exponential fitting scheme to predict an approximation, then use the three-step implicit exponential fittingscheme to correct this prediction. This combination is called the three-step predictor-corrector of exponential fittingmethod.The three-step predictor-corrector of exponential fitting method is applied to numerically compute the couplednonlinear Schrdinger equation and the nonlinear Schrdinger equation with varying coeffients.The numerical resultsshow that the scheme is highly accurate.