A four-step exponentially fitted method for the numerical solution of the Schrödinger equation

In this paper, we present an exponentially fitted four-step method for the numerical solution of the radial Schrödinger equation. More specifically we present a method that integrates exactly the functions {exp ( ±wx) , x {exp ( ±wx)}. We illustrated the efficiency of our newly produced scheme against well known methods, with excellent results. The numerical results showed that our method is considerably more efficient compared to well known methods used for the numerical solution of resonance problem of the radial Schrödinger equation.