Embedded eighth order methods for the numerical solution of the Schrödinger equation (Q1569733)

A new method for the approximate numerical integration of the radial Schrödinger equation is developed. The authors propose a family of eight-algebraic order explicit methods. Their complete phase-lag and stability analysis is developed. A simple error control mechanism, based on the phase-lag error, is described. Numerical results obtained for the phase-shift problems of the radial Schrödinger equation show the validity of the developed theory.