A new Numerov-type exponentially fitted method for the numerical integration of the Schrodinger equation

A new predictor-corrector exponentially fitted Numerov-type method is developed for the numerical integration of the radial Schrodinger equation and of coupled differential equations arising from the Schrodinger equation. The Numerov-type method considered contains free parameters which allow if to be fitted to exponential functions. The new fourth algebraic order method is 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 method is much more accurate than the other exponentially fitted methods. Based on the method developed in the present paper and on the method of Simos [24] a new variable-step procedure is developed for the numerical solution of the coupled differential equations arising from the Schrodinger equation. Numerical illustrations indicate that the new variable-step method is more efficient than other well known variable-step methods.