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.