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User-Friendly Expressions of the Coefficients of Some Exponentially Fitted Methods

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Computational Science and Its Applications – ICCSA 2020 (ICCSA 2020)

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Abstract

The purpose of this work consists in reformulating the coefficients of some exponentially-fitted (EF) methods with the aim of avoiding numerical cancellations and loss of precision. Usually the coefficients of an EF method are expressed in terms of \(\nu =\omega h\), where \(\omega \) is the frequency and h is the step size. Often, these coefficients exhibit a 0/0 indeterminate form when \(\nu \rightarrow 0\). To avoid this feature we will use two sets of functions, called C and S, which have been introduced by Ixaru in [61]. We show that the reformulation of the coefficients in terms of these functions leads to a complete removal of the indeterminacy and thus the convergence of the corresponding EF method is restored. Numerical results will be shown to highlight these properties.

The authors Conte, D’Ambrosio, Giordano and Paternoster are members of the GNCS group. This work is supported by GNCS-INDAM project and by PRIN2017-MIUR project.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Salerno, Fisciano, Salerno, Italy

    Dajana Conte, Giuseppe Giordano & Beatrice Paternoster

  2. Department of Information Engineering and Computer Science and Mathematics, University of L’Aquila, L’Aquila, Italy

    Raffaele D’Ambrosio

  3. Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest, Romania

    Liviu Gr. Ixaru

  4. Academy of Romanian Scientists, 54 Splaiul Independenţei, 050094, Bucharest, Romania

    Liviu Gr. Ixaru

Authors
  1. Dajana Conte
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  2. Raffaele D’Ambrosio
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  3. Giuseppe Giordano
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  4. Liviu Gr. Ixaru
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  5. Beatrice Paternoster
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Correspondence to Giuseppe Giordano .

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Editors and Affiliations

  1. University of Perugia, Perugia, Italy

    Osvaldo Gervasi

  2. University of Basilicata, Potenza, Potenza, Italy

    Beniamino Murgante

  3. Chair- Center of ICT/ICE, Covenant University, Ota, Nigeria

    Sanjay Misra

  4. University of Cagliari, Cagliari, Italy

    Chiara Garau

  5. University of Cagliari, Cagliari, Italy

    Ivan Blečić

  6. Clayton School of Information Technology, Monash University, Clayton, VIC, Australia

    David Taniar

  7. Department of Information Science, Kyushu Sangyo University, Fukuoka, Japan

    Bernady O. Apduhan

  8. University of Minho, Braga, Portugal

    Ana Maria A.C. Rocha

  9. Polytechnic University of Bari, Bari, Italy

    Eufemia Tarantino

  10. Polytechnic University of Bari, Bari, Italy

    Carmelo Maria Torre

  11. Department of Neurology, University of Massachusetts Medical School, Worcester, MA, USA

    Yeliz Karaca

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Conte, D., D’Ambrosio, R., Giordano, G., Ixaru, L.G., Paternoster, B. (2020). User-Friendly Expressions of the Coefficients of Some Exponentially Fitted Methods. In: Gervasi, O., et al. Computational Science and Its Applications – ICCSA 2020. ICCSA 2020. Lecture Notes in Computer Science(), vol 12249. Springer, Cham. https://doi.org/10.1007/978-3-030-58799-4_4

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