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New open modified trigonometrically-fitted Newton-Cotes type multilayer symplectic integrators for the numerical solution of the Schrödinger equation

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Abstract

In this paper we present new modified open Newton Cotes integrators and we develop a new modified trigonometrically-fitted open Newton-Cotes method. We study the connection between the new proposed schemes, the differential methods and the symplectic integrators. although The research on multistep symplectic integrators is very poor, although, much research has been done on one step symplectic integrators and several of then have obtained based on symplectic geometry. In this paper a new open modified numerical algorithm of Newton-Cotes type is produced. We present the new obtained method as symplectic multilayer integrator. The new obtained symplectic schemes are applied for the solution of the resonance problem of the radial Schrödinger Equation. The results show the efficiency of the new proposed algorithm.

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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

    Ibraheem Alolyan & T. E. Simos

  2. 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

  3. 10 Konitsis Street, Amfithea—Paleon Faliron, 175 64, Athens, 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 (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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Alolyan, I., Simos, T.E. New open modified trigonometrically-fitted Newton-Cotes type multilayer symplectic integrators for the numerical solution of the Schrödinger equation. J Math Chem 50, 782–804 (2012). https://doi.org/10.1007/s10910-011-9924-2

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