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Hybrid Multistep Multiderivative Methods for the Schr ¨odinger Equation and Related Problems

Authors:
Ibraheem Alolyan
Theodore Simos

Keywords: Numerical solution, Schr¨odinger equation, multistep methods, hybrid methods, multiderivative methods, interval of periodicity, P-stability, phase-lag, phase-fitted, derivatives of the phase-lag

Abstract:
In this paper we will present a new methodology for the development of efficient hybrid multiderivative multistep methods for the approximate solution of the Schr¨odinger equation and related initial-value or boundary-value problems with solutions, which their behavior is periodical or oscillating. The main characteristics of this new methodology are (1) the vanishing of the phase-lag on its level of the hybrid multiderivative method and (2) the vanishing of the its derivatives on its level of the hybrid multiderivative method. We apply the new methodology on a four-step hybrid type multiderivative method. A comparative error and stability analysis will be presented for the new produced method. The new constructed method will finally be applied to the resonance problem of the Schr¨odinger equation in order to show its efficiency.

Pages: 117 to 121

Copyright: Copyright (c) IARIA, 2013

Publication date: November 17, 2013

Published in: conference

ISSN: 2308-3484

ISBN: 978-1-61208-310-0

Location: Lisbon, Portugal

Dates: from November 17, 2013 to November 21, 2013