Simple and accurate explicit Bessel and Neumann fitted methods for the numerical solution of the Schrodinger equation

Explicit second and fourth algebraic order methods for the numerical soluti on of the Schrodinger equation are developed in this paper. The new methods have free parameters defined so that the methods are fitted to spherical B essel and Neumann functions. Based on these new methods we obtained a varia ble-step algorithm. The results produced based on the numerical solution of the radial Schrodinger equation and the coupled differential equations ari sing from the Schrodinger equation indicate that this new approach is more efficient than other well known ones.