THDRK methods with vanished phase-lag and its first derivative for the Schrödinger equation

Abstract

Two new optimized three-derivative Runge–Kutta type methods with vanishing phase-lag and its first derivative for the numerical integration of Schrodinger 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 Schrodinger equation with the Woods–Saxon potential.