An embedded Runge-Kutta method with phase-lag of order infinity for the numerical solution of the Schrödinger equation (Q2718397)

Based on a test equation Runge-Kutta methods of five and four algebraic orders are constructed characterized by total phase fitting (or phase-lag of order infinity) by the solution of a dispersion relation. The methods are applied to the one-dimensional (radial) Schrödinger equation in the forms of bound-states and the resonance problems as well as to coupled differential equations of Schrödinger type, and compared to other contemporary numerical methods. The efficiency of the proposed technique is documented.