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A new fourteenth algebraic order finite difference method for the approximate solution of the Schrödinger equation

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Abstract

In the present paper we will develop and analyse a new five-stages symmetric two-step method of high algebraic order with vanished phase-lag and its first, second, third, fourth and fifth derivatives. We will construct the new method. We will compute its local local truncation error (LTE). We will produce the asymptotic form of the LTE applying the new method to the radial time independent Schrödinger equation and we will compare it with other asymptotic forms of LTE of similar methods. Applying the new method to a scalar test equation with frequency different than the frequency of the scalar test equation used for the phase-lag analysis, we will investigate the stability and the interval of periodicity of the new method based and we will compare the produced interval of periodicity with other intervals of similar methods. Finally, we will examine the effectiveness of the new method applying it to the coupled Schrödinger equations.

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Authors and Affiliations

  1. School of Information Engineering, Chang’an University, Xi’an, 710064, People’s Republic of China

    Jianbin Zhao

  2. Group of Modern Computational Methods, Ural Federal University, 19 Mira Street, Ekaterinburg, 620002, Russian Federation

    T. E. Simos

  3. 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

  4. 10 Konitsis Street, Amfithea - Paleon Faliron, 175 64, Athens, Greece

    T. E. Simos

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T. E. Simos: 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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Zhao, J., Simos, T.E. A new fourteenth algebraic order finite difference method for the approximate solution of the Schrödinger equation. J Math Chem 55, 697–716 (2017). https://doi.org/10.1007/s10910-016-0704-x

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