A family of explicit linear six-step methods with vanished phase-lag and its first derivative

Abstract

A family of explicit linear sixth algebraic order six-step methods with vanished phase-lag and its first derivative is obtained in this paper. The investigation of the above family of methods contains: The theoretical study of the above mentioned family of methods contains: The application of the new family of linear six-step sixth algebraic order methods to the resonance problem of the one-dimensional time independent Schrodinger equation is used for the computational study of the new family of methods. The result of the above mentioned theoretical and computational investigation is that the new proposed family of linear explicit schemes are computationally and theoretically more effective than other well known methods for the approximate solution of the radial Schrodinger equation and related initial or boundary value problems with periodic and/or oscillating solutions.