An embedded phase-fitted modified Runge-Kutta method for the numerical integration of the radial Schrödinger equation

A new way for constructing efficient embedded modified Runge-Kutta methods for the numerical solution of the Schrödinger equation is presented in this Letter. The methods of the embedded scheme have algebraic orders five and four. Applications of the new pair to several problems arising from the radial Schrödinger equation indicate that the new pair is more efficient than other well known comparable embedded Runge-Kutta pairs.