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

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Abstract

A study on the vanishing of the phase-lag and its first and second derivatives for a family of explicit four-step methods first introduced by Anastassi and Simos (J Comput Appl Math 236:3880–3889, 2012) is presented in this paper. The methods investigated in this paper belongs to the category of methods with frequency dependent coefficients. For these methods we will investigate the procedure of vanishing of the phase-lag and its first and second derivatives. For the new proposed methods we will define the local truncation error and we will study an local truncation error analysis. Finally we will compare the results of the error analysis with other known methods of the literature. We will study also the stability analysis of the new proposed method. We will apply the new produced methods on the resonance problem of the Schrödinger equation in order to investigate their efficiency.

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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. 4 with constant coefficients.

  3. The reference values are computed using the well known two-step method of Chawla and Rao [14] 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, Tripolis, 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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Highly Cited Researcher (http://highlycited.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. A new explicit four-step method with vanished phase-lag and its first and second derivatives. J Math Chem 53, 402–429 (2015). https://doi.org/10.1007/s10910-014-0431-0

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  • DOI: https://doi.org/10.1007/s10910-014-0431-0

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