Exponentially fitted Runge–Kutta methods for the numerical solution of the Schrödinger equation and related problems

Exponentially fitted Runge–Kutta methods for the numerical integration of the radial Schrödinger equation or systems of equations of the Schrödinger type and for the numerical solution of other related initial-value problems with periodic or oscillating solutions are developed in this paper. Numerical and theoretical results obtained for several well-known problems show the efficiency of the new methods.