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An explicit four-step method with vanished phase-lag and its first and second derivatives

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Abstract

In this paper we will develop an explicit fourth algebraic order four-step method with phase-lag and its first and second derivatives vanished. The comparative error and the stability analysis of the above mentioned paper is also presented. The new obtained method is applied on the resonance problem of the Schrödinger equationIn order in order to examine its efficiency. The theoretical and the computational results shown that the new obtained method is more efficient than other well known methods for the numerical solution of the Schrödinger equation and related initial-value or boundary-value problems with periodic and/or oscillating solutions.

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Notes

  1. Where \(S\) is a set of distinct points

  2. With the term classical we mean the method of Sect. 3 with constant coefficients

  3. The reference values are computed using the well known two-step method of Chawla and Rao [28] with small step size for the integration

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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

    T. E. Simos

  2. Laboratory of Computational Sciences, Department of Informatics and Telecommunications, Faculty of Economy, Management and Informatics, 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. T. E. Simos
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T. E. Simos is an 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. An explicit four-step method with vanished phase-lag and its first and second derivatives. J Math Chem 52, 833–855 (2014). https://doi.org/10.1007/s10910-013-0296-7

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  • DOI: https://doi.org/10.1007/s10910-013-0296-7

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