Six-Step Methods with Vanished Phase-Lag and its First Derivatives for the Approximate Solution of the Schrodinger Equation and Related Problems

摘要

Two six-step methods for the approximate solution of second order periodic initial or boundary-value problems are studied in this paper. The development of the new proposed methods is based on the vanishing phase-lag and its first derivative. We studied the error for the two produced methods and we compared it with the error of the corresponding method with constant coefficients. We also investigated the stability for the two obtained methods. We applied the new obtained method to the resonance problem of the radial time independent Schrodinger equation in order to show their efficiency.