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Trigonometric-Fitted Explicit Numerov-Type Method with Vanishing Phase-Lag and Its First and Second Derivatives

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Abstract

An effectively four-stage, sixth-order, hybrid explicit Numerov-type method is presented for the solution of the special second-order initial value problem. The new method uses variable step, is trigonometric fitted and the phase-lag is nullified along with its first and second derivative. Extensive numerical tests illustrate the superiority of our proposal over similar methods found in the relevant literature.

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Authors and Affiliations

  1. Department of Automation Engineering, TEI of Sterea Hellas, Psahna Campus, 34400, Psachna, Greece

    Ch. Tsitouras & T. E. Simos

  2. Department of Mathematics, College of Sciences, King Saud University, P. O. Box 2455 , Riyadh, 11451, Saudi Arabia

    T. E. Simos

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

    T. E. Simos

  4. Section of Mathematics, Department of Civil Engineering, Democritus University of Thrace, Xanthi, Greece

    T. E. Simos

  5. 10 Konitsis St., 17564, Athens, Greece

    T. E. Simos

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  1. Ch. Tsitouras
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  2. T. E. Simos
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Correspondence to T. E. Simos.

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Tsitouras, C., Simos, T.E. Trigonometric-Fitted Explicit Numerov-Type Method with Vanishing Phase-Lag and Its First and Second Derivatives. Mediterr. J. Math. 15, 168 (2018). https://doi.org/10.1007/s00009-018-1216-7

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