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Global error estimation for explicit second derivative general linear methods

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Abstract

In this paper, we describe an approach to estimate the global error for explicit second derivative general linear methods based on the approach which has been already used for global error estimation of explicit general linear methods. In this approach, to estimate the global error, we use the numerical solutions of pairs of second derivative general linear methods with the same order and stage order that are constructed such that their global error functions are proportional. Numerical experiments demonstrate the excellent agreement of the global error estimation with the exact one in both constant and variable stepsize environments.

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Funding

The work of the first and second authors was supported by the University of Tabriz, International and Academic Cooperation Directorate, in the framework of TabrizU-300 program.

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Authors and Affiliations

  1. Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran

    Ali Abdi & Gholamreza Hojjati

  2. Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università di Napoli Federico II, Napoli, Italy

    Giuseppe Izzo

  3. School of Mathematical & Statistical Sciences, Arizona State University, Tempe, 85287, AZ, USA

    Zdzislaw Jackiewicz

  4. Department of Applied Mathematics, AGH University of Science and Technology, Kraków, Poland

    Zdzislaw Jackiewicz

Authors
  1. Ali Abdi
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  2. Gholamreza Hojjati
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  3. Giuseppe Izzo
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  4. Zdzislaw Jackiewicz
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Correspondence to Ali Abdi.

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Abdi, A., Hojjati, G., Izzo, G. et al. Global error estimation for explicit second derivative general linear methods. Numer Algor 90, 833–850 (2022). https://doi.org/10.1007/s11075-021-01211-9

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  • DOI: https://doi.org/10.1007/s11075-021-01211-9

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Mathematics Subject Classification (2010)