Novel exponentially fitted two-derivative Runge–Kutta methods for solving the radial Schrödinger equation

A family of new exponentially fitted two-derivative Runge–Kutta (TDRK) methods with exponential order up to two for solving the Schrödinger equation is obtained in this paper. Error analysis is conducted in terms of the asymptotic expressions of the energy. Linear stability and phase properties are analyzed. 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 Schrödinger equation with the Woods-Saxon potential.