Trigonometrically fitted Runge-Kutta methods for the numerical solution of the Schrodinger equation

In this paper we construct two trigonometrically fitted methods based on a classical Runge-Kutta method of England with fifth algebraic order. The methods will be used for the integration of the radial Schrodinger equation and have high efficiency as the results show. The efficiency is higher when using higher energy and this can be explained by the error analysis of the methods. More specifically the new methods have lower powers of the energy in the local truncation error and that keeps the error at lower values.