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

A family of predictor-corrector exponential Numerov-type 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 very simple and integrate more exponential functions than both the well-known fourth-order Numerov-type exponentially fitted methods and the sixth algebraic order Runge-Kutta-type methods. Numerical results also indicate that the new methods are much more accurate than the other exponentially fitted methods mentioned above.