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Jacobian-Dependent Two-Stage Peer Method for Ordinary Differential Equations

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Computational Science and Its Applications – ICCSA 2021 (ICCSA 2021)

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Abstract

In this paper we derive new explicit two-stage peer methods for the numerical solution of ordinary differential equations by using the technique introduced in [2] for Runge-Kutta methods. This technique allows to re-determine the order conditions of classical methods, obtaining new coefficients values. The coefficients of new methods are no longer constant, but depend on the Jacobian function of the ordinary differential equation. The new methods preserve the order of classical peer methods, and are more accurate and with better stability properties. Numerical tests highlight the advantage of new methods especially for stiff problems.

The authors Conte, Pagano 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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Authors and Affiliations

  1. Department of Mathematics, University of Salerno, Via Giovanni Paolo II, 132 - 84084, Fisciano, SA, Italy

    Dajana Conte, Giovanni Pagano & Beatrice Paternoster

Authors
  1. Dajana Conte
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  2. Giovanni Pagano
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  3. Beatrice Paternoster
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Corresponding author

Correspondence to Giovanni Pagano .

Editor information

Editors and Affiliations

  1. University of Perugia, Perugia, Italy

    Osvaldo Gervasi

  2. University of Basilicata, Potenza, Potenza, Italy

    Beniamino Murgante

  3. Covenant University, Ota, Nigeria

    Sanjay Misra

  4. University of Cagliari, Cagliari, Italy

    Chiara Garau

  5. University of Cagliari, Cagliari, Italy

    Ivan Blečić

  6. Monash University, Clayton, VIC, Australia

    David Taniar

  7. 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

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Conte, D., Pagano, G., Paternoster, B. (2021). Jacobian-Dependent Two-Stage Peer Method for Ordinary Differential Equations. In: Gervasi, O., et al. Computational Science and Its Applications – ICCSA 2021. ICCSA 2021. Lecture Notes in Computer Science(), vol 12949. Springer, Cham. https://doi.org/10.1007/978-3-030-86653-2_23

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  • DOI: https://doi.org/10.1007/978-3-030-86653-2_23

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-86652-5

  • Online ISBN: 978-3-030-86653-2

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