A family of RK4(4) methods with zero phase-lag and deriνatiνes for the numerical solution of the Schrödinger equation

We construct a family of two new optimized explicit Runge-Kutta methods with zero phase-lag and derivatives for the numerical solution of the time-independent radial Schrödinger equation with oscillating solutions. We present also the stability analysis of the new method and the relation of the interval of periodicity with the frequency of the new developed method. The numerical results show the superiority of the new technique of nullifying both the phase-lag and its derivatives.