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A new hybrid two-step method with vanished phase-lag and its first and second derivatives for the numerical solution of the Schrödinger equation and related problems

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Abstract

The maximization of the efficiency of a hybrid two-step method for the numerical solution of the radial Schrödinger equation and related problems with periodic or oscillating solutions via the procedure of vanishing of the phase-lag and its derivatives is studied in this paper. More specifically, we investigate the vanishing of the phase-lag and its first and second derivatives and how this disappearance maximizes the efficiency of the hybrid two-step method.

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Authors and Affiliations

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

    Ibraheem Alolyan & T. E. Simos

  2. Laboratory of Computational Sciences, Department of Computer Science and Technology, Faculty of Sciences and Technology, University of Peloponnese, 221 00, Tripoli, Greece

    T. E. Simos

  3. 10 Konitsis Street, Amfithea—Paleon Faliron, 175 64, Athens, Greece

    T. E. Simos

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  1. Ibraheem Alolyan
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T. E. Simos: Highly Cited Researcher (http://isihighlycited.com/), Active Member of the European Academy of Sciences and Arts. Active Member of the European Academy of Sciences. Corresponding Member of European Academy of Arts, Sciences and Humanities.

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Alolyan, I., Simos, T.E. A new hybrid two-step method with vanished phase-lag and its first and second derivatives for the numerical solution of the Schrödinger equation and related problems. J Math Chem 50, 1861–1881 (2012). https://doi.org/10.1007/s10910-012-0008-8

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