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A hybrid finite difference pair with maximum phase and stability properties

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Abstract

We develop, in the present paper and for the first time in the literature, a new hybrid finite difference pair of symmetric two-step. The basic properties of the new pair are:

  • is of symmetric form,

  • is of two-step,

  • is of four-stages,

  • is of tenth-algebraic order,

  • the development of the hybrid symmetric two-step pair is of the following form:

    • first layer is an approximation on the point \(x_{n-1}\),

    • second layer is an approximation on the point \(x_{n-1}\),

    • third layer is an approximation on the point \(x_{n}\) and finally,

    • fourth layer is an approximation on the point \(x_{n+1}\),

  • it has vanished the phase-lag and its first, second and third derivatives,

  • it has excellent stability properties,

  • it has an interval of periodicity equal to \(\left( 0, \infty \right) \).

For the new symmetric finite difference pair a full analysis is presented. We evaluate the efficiency of the new obtained symmetric finite difference pair by applying it on systems of coupled differential equations of the Schrödinger form.

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Authors and Affiliations

  1. School of Electronics and Information Engineering, Fuqing Branch of Fujian Normal University, Fuqing, 350300, People’s Republic of China

    Jie Fang

  2. Department of Computer Science and Technology, Neusoft Institute Guangdong, Foshan, 528228, China

    Chenglian Liu

  3. 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

  4. 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

  5. 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. Working in part time in Department of Informatics and Telecommunications, Faculty of Economy, Management and Informatics, University of Peloponnese, Greece.

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Fang, J., Liu, C. & Simos, T.E. A hybrid finite difference pair with maximum phase and stability properties. J Math Chem 56, 423–448 (2018). https://doi.org/10.1007/s10910-017-0793-1

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