On variable-step methods for the numerical solution of Schrödinger equation and related problems

In this paper we present a review for the construction of variable-step methods for the numerical integration of the Schrödinger equation. Phase-lag and stability are investigated. The methods are variable-step because of a simple natural error control mechanism. Numerical results obtained for coupled differential equations arising from the Schrödinger equation and for the wave equation show the validity of the approach presented.