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Two new optimized three-derivative Runge–Kutta type methods with vanishing phase-lag and its first derivative for the numerical integration of Schrödinger equation are derived in this paper. We present the error analysis in terms of the asymptotic expressions of the local errors. Numerical results are reported to show the efficiency and robustness of the new methods for the numerical integration of the Schrödinger equation with the Woods–Saxon potential. [ABSTRACT FROM AUTHOR]

A family of modified two-derivative Runge–Kutta (MTDRK) methods for the integration of the Schrödinger equation are obtained. Two new three-stage and fifth order TDRK methods are derived. The numerical results in the integration of the radial Schrödinger equation with the Woods–Saxon potential are reported to show the high efficiency of our new methods. The results of the error analysis are illustrated by the resonance problem. [ABSTRACT FROM AUTHOR]

Two exponentially fitted two-derivative Runge-Kutta pairs for the numerical integration of the Schrödinger equation are presented in this paper. The asymptotic expressions of the local errors for large energies are given. The numerical results in the integration of the radial Schrödinger equation with the Woods-Saxon potential and the Lennard-Jones potential show the high efficiency of our new methods when compared with some famous optimized codes in the literature. [ABSTRACT FROM AUTHOR]