A family of fifth algebraic order trigonometrically fitted Runge-Kutta methods for the numerical solution of the Schrödinger equation

A family of trigonometrically fitted Runge-Kutta methods for the numerical integration of the radial Schrödinger equation is developed. Theoretical and numerical results obtained for the radial Schrödinger equation and for the well known Woods-Saxon potential and for the coupled differential equations of the Schrödinger type show the efficiency of the new method.