Abstract
A family of predictor-corrector exponential Numerov-type methods is developed for the numerical integration of the one-dimensional Schrödinger equation. The Numerov-type methods considered contain free parameters which allow it to be fitted to exponential functions. The new fourth algebraic order 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.
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