Mulitstep methods with vanished phase-lag and its first and second derivatives for the numerical integration of the Schrödinger equation

A tenth algebraic order eight-step method is developed in this paper. For this method  we require the phase-lag and its first and second derivatives to be vanished. A comparative error analysis and a comparative stability analysis are also presented in this paper. The new proposed method is applied for the numerical solution of the one-dimensional Schrödinger equation. The efficiency of the new methodology is proved via the theoretical analysis and the numerical applications. General conclusions about the importance of several properties on the construction of numerical algorithms for the approximate solution of the radial Schrödinger equation are also presented.