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We construct a family of two new optimized explicit Runge-Kutta methods withzero phase-lag and derivatives for the numerical solution of thetime-independent radial Schr\"odinger equation and related ordinarydifferential equations with oscillating solutions. The numerical results showthe superiority of the new technique of nullifying both the phase-lag and itsderivatives.

A Family of Runge-Kutta Methods with Zero Phase-Lag and Derivatives for the Numerical Solution of the Schr\"odinger Equation and Related Problems