LAUSR

A new embedded 4(3) pair of modified two-derivative Runge–Kutta (TDRK) methods with First Same As Last (FSAL) property for the numerical solution of the Schrödinger equation is constructed in this paper. Both the error analysis and phase properties indicate good accuracy of the new pair especially for large eigenvalues. An application to the well-known Lennard-Jones potential confirms the theory and shows that the new pair is more efficient than some high-quality Runge–Kutta(–Nyström) pairs in the literature.