A New Optimized Runge-Kutta Pair for the Numerical Solution of the Radial Schrödinger Equation

Abstract EN

A new embedded pair of explicit modified Runge-Kutta (RK) methods for the numerical integration of the radial Schrödinger equation is presented.

The two RK methods in the pair have algebraic orders five and four, respectively.

The two methods of the embedded pair are derived by nullifying the phase lag, the first derivative of the phase lag of the fifth-order method, and the phase lag of the fourth-order method.

Nu merical experiments show the efficiency and robustness of our new methods compared with some well-known integrators in the literature.