Modified explicit Runge–Kutta methods for the numerical solution of the Schrödinger equation

摘要

A new procedure for constructing Runge–Kutta methods for an efficient integration of the radial Schrödinger equation is developed in this paper. The new modified Runge–Kutta methods are of algebraically order four. The asymptotic expressions of the local errors for large energies are discussed. Numerical results obtained for the widely used Woods–Saxon potential show the efficiency of the new methods compared with other special optimized fourth-order Runge–Kutta methods. The error analysis will be clearly confirmed by the resonance problem.