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A High-Order Two-Step Phase-Fitted Method for the Numerical Solution of the Schrödinger Equation

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Abstract

In this paper, we will develop a four-stage high algebraic order symmetric two-step method with vanished phase-lag and its first up to the fourth derivative. For the proposed method, we will study the following: the phase-lag analysis of the new method; the development of the new method; the local truncation error analysis which is based on the radial Schrödinger equation; the stability and the interval of periodicity analysis which is based on a scalar test equation with frequency different than the frequency of the scalar test equation used for the phase-lag analysis; the error estimation procedure which is based on the algebraic order; and the numerical results from our numerical tests for the examination of the efficiency of the new obtained method. The numerical tests are based on the numerical solution of the Schrödinger equation.

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Authors and Affiliations

  1. School of Information Engineering, Chang’an University, Xi’an, 710064, China

    Wei Zhang

  2. China Highway Engineering Consulting Group Company LTD., Beijing, 100097, China

    Wei Zhang

  3. Department of Mathematics, College of Sciences, King Saud University, P. O. Box 2455, Riyadh, 11451, Saudi Arabia

    T. E. Simos

  4. Laboratory of Computational Sciences, Department of Informatics and Telecommunications, Faculty of Economy, Management and Informatics, University of Peloponnese, GR-221 00, Tripolis, Greece

    T. E. Simos

  5. 10 Konitsis Street, Amfithea-Paleon Faliron, 175 64, Athens, Greece

    T. E. Simos

Authors
  1. Wei Zhang
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  2. T. E. Simos
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Correspondence to T. E. Simos.

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Highly Cited Researcher (http://highlycited.com/), Active member of the European Academy of Sciences. Active member of the European Academy of Sciences and Arts. Corresponding Member of the of European Academy of Arts, Sciences and Humanities.

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Zhang, W., Simos, T.E. A High-Order Two-Step Phase-Fitted Method for the Numerical Solution of the Schrödinger Equation. Mediterr. J. Math. 13, 5177–5194 (2016). https://doi.org/10.1007/s00009-016-0800-y

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  • DOI: https://doi.org/10.1007/s00009-016-0800-y

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