Bessel and Neumann fitted methods for the numerical solution of the Schrödinger equation

The Bessel and Neumann fitted methods for the numerical solution of the Schrödinger equation is the subject of this paper. An eighth-algebraic-order method for the numerical solution of the Schrödinger equation is developed in this paper. The new method has free parameters which are defined such that the method is fitted to spherical Bessel and Neumann functions. A variable-step procedure is obtained based on the newly developed method and the method of Simos [1]. The results produced based on the numerical solution of the radial Schrödinger equation and of coupled differential equations arising from the Schrödinger equation indicate that this new approach is more efficient than other well-known methods.