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A new high order two-step method with vanished phase-lag and its derivatives for the numerical integration of the Schrödinger equation

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Abstract

In this paper we develop a new hybrid method of high order with phase-lag and its first, second and third derivatives equal to zero. For the produced method we study its error and stability. We apply the newly obtained method to the Schrödinger equation. The application shows the efficiency of the new produced method.

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Authors and Affiliations

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

    Ibraheem Alolyan

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

    T. E. Simos

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

    T. E. Simos

  4. 10 Konitsis Street, Amfithea—Paleon Faliron, 175 64, Athens, Greece

    T. E. Simos

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  1. Ibraheem Alolyan
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Correspondence to T. E. Simos.

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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 high order two-step method with vanished phase-lag and its derivatives for the numerical integration of the Schrödinger equation. J Math Chem 50, 2351–2373 (2012). https://doi.org/10.1007/s10910-012-0035-5

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