A family of hybrid exponentially fitted predictor-corrector methods for the numerical integration of the radial Schrِdinger equation

A family of hybrid, exponentially fitted, predictor-corrector methods is developed for the numerical integration of the one-dimensional Schrِdinger equation. The formula considered contains certain free parameters which allow it to be fitted automatically to exponential functions. The new methods are of algebraic order six, they are very simple and integrate more exponential functions than both the well-known fourth-order Numerov-type exponentially fitted methods and the Runge-Kutta-type methods of algebraic order six. Numerical results also indicate that the new methods are much more accurate than the other exponentially fitted methods mentioned above.