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A modified phase-fitted and amplification-fitted Runge-Kutta-Nyström method for the numerical solution of the radial Schrödinger equation

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Abstract

A new Runge-Kutta-Nyström method, with phase-lag and amplification error of order infinity, for the numerical solution of the Schrödinger equation is developed in this paper. The new method is based on the Runge-Kutta-Nyström method with fourth algebraic order, developed by Dormand, El-Mikkawy and Prince. Numerical illustrations indicate that the new method is much more efficient than other methods derived for the same purpose.

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Acknowledgements

We want to thank the anonymous reviewers for their careful reading of the manuscript and their fruitful comments and suggestions.

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Authors and Affiliations

  1. Department of Computer Science and Technology, Faculty of Sciences and Technology, University of Peloponnese, GR-22 100, Tripolis, Greece

    D. F. Papadopoulos & T. E. Simos

  2. Department of Finance and Auditing, School of Management and Economics, Technological Educational Institute of Kalamata, GR-241 00, Antikalamos, Greece

    Z. A. Anastassi

Authors
  1. D. F. Papadopoulos
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  2. Z. A. Anastassi
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  3. T. E. Simos
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Correspondence to T. E. Simos.

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Prof. Dr. Simos is a 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, Address: Dr. T. E. Simos, 10 Konitsis Street, Amfithea - Paleon Faliron, GR-175 64 Athens, GREECE Tel: 0030 210 94 21 510, e-mail: tsimos.conf@gmail.com

T. E. Simos, On sabbatical leave to Department of Chemistry, School of Sciences, University of Patras.

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Papadopoulos, D.F., Anastassi, Z.A. & Simos, T.E. A modified phase-fitted and amplification-fitted Runge-Kutta-Nyström method for the numerical solution of the radial Schrödinger equation. J Mol Model 16, 1339–1346 (2010). https://doi.org/10.1007/s00894-009-0626-7

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  • DOI: https://doi.org/10.1007/s00894-009-0626-7

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