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New high order multiderivative explicit four-step methods with vanished phase-lag and its derivatives for the approximate solution of the Schrödinger equation. Part I: Construction and theoretical analysis

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Abstract

In this paper we develop and study new high algebraic order multiderivative explicit four-step method with phase-lag and its first, second and third derivatives equal to zero. For the produced methods we investigate their errors and stability. Based on the above mentioned analysis we will arrive to some remarks and conclusions about their the efficiency to the numerical integration of the radial Schrödinger equation.

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Authors and Affiliations

  1. 10 Konitsis Street, Amfithea-Paleon Faliron, 175 64, Athens, Greece

    T. E. Simos

  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, Tripoli, Greece

    T. E. Simos

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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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Simos, T.E. New high order multiderivative explicit four-step methods with vanished phase-lag and its derivatives for the approximate solution of the Schrödinger equation. Part I: Construction and theoretical analysis. J Math Chem 51, 194–226 (2013). https://doi.org/10.1007/s10910-012-0074-y

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  • DOI: https://doi.org/10.1007/s10910-012-0074-y

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