New high order multiderivative explicit four-step methods with vanished phase-lag and its derivatives for the approximate solution of the Schrödinger equation. Part I: Construction and theoretical analysis

Abstract

In this paper we develop and study new high algebraic order multiderivative explicit four-step method with phase-lag and its first, second and third derivatives equal to zero. For the produced methods we investigate their errors and stability. Based on the above mentioned analysis we will arrive to some remarks and conclusions about their the efficiency to the numerical integration of the radial Schrodinger equation.