A sixth order Bessel and Neumann fitted method for the numerical solution of the Schrodinger equation

A sixth algebraic order method for the numerical solution of the Schrodinger equation is developed in this paper. The new method has free parameters which will be defined such that the method is fitted to spherical Bessel and Neumann functions. Based on the new method and the method of Simos and Williams [15] we have obtained a variable-step method. The results produced based on the numerical solution the radial Schrodinger equation and of coupled differential equations arising from the Schrodinger equation indicate that this new approache is more efficient than other well known methods.