A family of four-step exponentially fitted predictor-corrector methods for the numerical integration of the Schrِdinger equation

A family of predictor-corrector exponential four-step methods is developed for the numerical integration of the one-dimensional Schrِdinger equation. The formula developed contains certain free parameters which allows it to be fitted automatically to exponential functions. The new methods integrate more exponential functions and are very simple compared with the well-known sixth algebraic order Runge-Kutta-type methods. Numerical results indicate that the new method is much more accurate than other exponentially fitted methods.