A new phase-fitted modified Runge–Kutta pair for the numerical solution of the radial Schrödinger equation

A new embedded pair of phase-fitted explicit modified Runge–Kutta (RK) methods for the numerical integration of the radial Schrödinger equation is presented in this paper. The two component methods in the pair have algebraic order five and four, respectively. The new fifth-order method is shown to have the phase-lag constant of one order higher than that in Van de Vyver’s RK5(4) pair (Van de Vyver (2006) [5]) when the fitting frequency is close to the real frequency. The numerical results in the integration of the radial Schrödinger equation are reported showing the higher efficiency of the new fifth-order modified RK method and the new modified RK5(4) pair compared to some highly efficient methods in the recent literature.