EXPONENTIAL FITTED METHODS FOR THE NUMERICAL-INTEGRATION OF THE SCHRODINGER-EQUATION

A new sixth-order Runge-Kutta type method is developed for the numerical integration of the one-dimensional Schrodinger equation. The formula developed contains certain free parameters which allows it to be fitted automatically to exponential functions. We give a comparative error analysis with other sixth-order exponentially fitted methods. The theoretical and numerical results indicate that the new method is more accurate than the other exponentially fitted methods.