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Hybrid high algebraic order two-step method with vanished phase-lag and its first, second, third, fourth and fifth derivatives

Author

Listed:
  • Junyan Ma

    (School of Information Engineering, Changan University, 710064 Xian, Shaanxi, P. R. China)

  • T. E. Simos

    (Department of Mathematics, College of Sciences, King Saud University, P. O. Box 2455, Riyadh 11451, Saudi Arabia3Laboratory of Computational Sciences, Department of Informatics and Telecommunications, Faculty of Economy, Management and Informatics, University of Peloponnese, GR-221 00 Tripolis, Greece)

Abstract

A hybrid tenth algebraic order two-step method with vanished phase-lag and its first, second, third, fourth and fifth derivatives are obtained in this paper. We will investigate•the construction of the method•the local truncation error (LTE) of the newly obtained method. We will also compare the lte of the newly developed method with other methods in the literature (this is called the comparative LTE analysis)•the stability (interval of periodicity) of the produced method using frequency for the scalar test equation different from the frequency used in the scalar test equation for phase-lag analysis (this is called stability analysis)•the application of the newly obtained method to the resonance problem of the Schrödinger equation. We will compare its effectiveness with the efficiency of other known methods in the literature.It will be proved that the developed method is effective for the approximate solution of the Schrödinger equation and related periodical or oscillatory initial value or boundary value problems.

Suggested Citation

  • Junyan Ma & T. E. Simos, 2016. "Hybrid high algebraic order two-step method with vanished phase-lag and its first, second, third, fourth and fifth derivatives," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 27(05), pages 1-20, May.
    • Handle: RePEc:wsi:ijmpcx:v:27:y:2016:i:05:n:s0129183116500492
    DOI: 10.1142/S0129183116500492
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    Cited by:

    1. Tsitouras, Ch. & Famelis, I.Th., 2018. "Bounds for variable degree rational L∞ approximations to the matrix exponential," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 376-386.
    2. Tsitouras, Ch., 2019. "Explicit Runge–Kutta methods for starting integration of Lane–Emden problem," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 353-364.
    3. Saleem Obaidat & Said Mesloub, 2019. "A New Explicit Four-Step Symmetric Method for Solving Schrödinger’s Equation," Mathematics, MDPI, vol. 7(11), pages 1-12, November.

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