Implicit three-step methods with phase-lag and its derivatives equal to zero for the numerical solution of the Schrödinger equation and related problems

Abstract

Articles you may be interested inA linear four-step method with vanished phase-lag and its first and second derivatives for the numerical solution of periodic initial and/or boundary value problems AIP Conf. Proc. 1618, 1031 (2014); 10.1063/1.4897910 Six-step methods with vanished phase-lag and its first derivatives for the approximate solution of the Schrödinger equation and related problems AIP Conf. Proc. 1618, 1026 (2014); 10.1063/1.4897909Four-step hybrid type methods with vanished phase-lag and its derivatives for each level for the numerical solution of the Schrödinger equation and related problems AIP Conf. Abstract.A family of implicit three-step methods for the numerical solution of special second order periodic initial or boundary-value problems (without rst derivative in their mathematical model) is investigated in this paper. The construction of the methods of the present family is based on the request phase-lag and its derivatives to be equal to zero. The study of the methods of the present family included • the investigation on the local truncation error of the methods and its comparison with the local truncation error of the corresponding methods with constant coef cients • the investigation on the stability for the new produced methods (using scalar test equation with frequency different than the scalar test equation for the phase-lag analysis) • the application of the new constructed methods to the resonance problem of the radial time independent Schrödinger equation in order to show their ef ciency.