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A family of ten-step methods with vanished phase-lag and its first derivative for the numerical solution of the Schrödinger equation

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Abstract

A family of high algebraic order ten-step methods is obtained in this paper. The new developed methods have vanished phase-lag (the first one) and phase-lag and its first derivative (the second one). We apply the new developed methods to the resonance problem of the radial Schrödinger equation. The efficiency of the new proposed methods is shown via error analysis and numerical applications.

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

    Ibraheem Alolyan & T. E. Simos

  2. 10 Konitsis Street, Amfithea—Paleon Faliron, 175 64, Athens, Greece

    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

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

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Highly Cited Researcher, 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 family of ten-step methods with vanished phase-lag and its first derivative for the numerical solution of the Schrödinger equation. J Math Chem 49, 1843–1888 (2011). https://doi.org/10.1007/s10910-011-9862-z

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  • DOI: https://doi.org/10.1007/s10910-011-9862-z

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