New optimized two-derivative Runge-Kutta type methods for solving the radial Schrödinger equation

Abstract

This paper focuses on adapted two-derivative Runge-Kutta (TDRK) type methods for solving the Schrodinger equation. Two new TDRK methods are derived by nullifying their phase-lags and the first derivatives of the phase-lags. Error analysis is carried out by means of asymptotic expressions of the local errors. Numerical results are reported to show the efficiency and robustness of the new methods in comparison with some RK type methods specially tuned to the integration of the radial time-independent Schrodinger equation with the Woods–Saxon potential.