Symmetric Three-Stages Eight-Step Embedded Methods (S3SESM) with Eliminated Phase-lag and its Derivatives for the Numerical Solution of Second Order Problems

摘要

A family of symmetric three-stages eight-step embedded (S3SESME) methods with eliminated phase-lag and its derivatives are described in this paper. Since the methods have three stages are belonged to the category of hybrid methods. For the new proposed family of methods we request elimination of the phase-lag and its derivatives. We note here that for this specific family of embedded pairs the phase-lag and the stability analysis are studied on the whole scheme and no on each stage of each scheme. The obtained families of embedded pairs are applied on the approximate solution of the Schrodinger equation and other related problems. The theoretical and numerical achievements show the effectiveness of the new developed embedded pairs.