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A finite difference pair with improved phase and stability properties

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Abstract

A new finite difference pair is produced in this paper, for the first time in the literature. The characteristics of the new finite diffence pair are: (1) is of symmetric two-step, (2) is four-stages, (3) is of tenth-algebraic order, (4) the production of the pair is based on the following approximations for the layers: first and second layer are approximated on the point \(x_{n-1}\), third layer is approximated on the point \(x_{n}\) and finally fourth layer is approximated on the point \(x_{n+1}\), (5) has vanished the phase-lag and its first and second derivatives, (6) has excellent stability properties for all type of problems, (7) has an interval of periodicity equal to \(\left( 0, \infty \right) \). We present for the new obtained finite difference pair a full theoretical analysis. The effectiveness of the new developed finite difference pair is proved by its application on systems of coupled differential equations arising from the Schrödinger equation.

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

    Ke Yan

  2. Data Recovery Key Laboratory of Sichuan Province, College of Mathematics and Information Science, Neijiang Normal University, Neijiang, 641100, People’s Republic of China

    T. E. Simos

  3. 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

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

    T. E. Simos

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T. E. Simos did his Part time in the University of Peloponnese.

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Yan, K., Simos, T.E. A finite difference pair with improved phase and stability properties. J Math Chem 56, 170–192 (2018). https://doi.org/10.1007/s10910-017-0787-z

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