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The barycentric rational numerical differentiation formulas for stiff ODEs and DAEs

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Abstract

Due to their several attractive properties, BDF-type multistep methods are usually the method-of-choice for solving stiff initial value problems (IVPs) of ordinary differential equations (ODEs) and differential-algebraic equations (DAEs). Recently, a class of BDF-type methods based on linear barycentric rational interpolants (LBRIs), referred to as RBDF methods, was introduced for solving ODEs. In the present paper, we are going to introduce a new family of LBRIs-based BDF-type formulas for the numerical solution of ODEs and DAEs with desirable stability properties and smaller error constants than those of the RBDF methods. Numerical experiments of the proposed methods on some well-known IVPs for ODEs and DAEs with index \({\le }{3}\) illustrate the efficiency and capability of the methods in solving such problems.

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Acknowledgements

The first author wish to express his gratitude to M. Arnold and H. Podhaisky for making his visit to Martin-Luther-Universität Halle-Wittenberg possible.

Funding

The results reported in this paper were obtained during the visit of the first author to Martin-Luther-Universität Halle-Wittenberg in \(2022-2023\), which was supported by the Alexander von Humboldt Foundation (Germany).

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Author notes

  1. Ali Abdi

    Present address: Institut für Mathematik, Martin-Luther-Universität Halle-Wittenberg, Halle (Saale), Germany

Authors and Affiliations

  1. Faculty of Mathematics, Statistics and Computer Science, University of Tabriz, Tabriz, Iran

    Ali Abdi

  2. Research Department of Computational Algorithms and Mathematical Models, University of Tabriz, Tabriz, Iran

    Ali Abdi

  3. Institut für Mathematik, Martin-Luther-Universität Halle-Wittenberg, Halle (Saale), Germany

    Martin Arnold & Helmut Podhaisky

Authors
  1. Ali Abdi
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All authors wrote the main manuscript text, and all authors reviewed the manuscript.

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Correspondence to Ali Abdi.

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Abdi, A., Arnold, M. & Podhaisky, H. The barycentric rational numerical differentiation formulas for stiff ODEs and DAEs. Numer Algor 97, 431–451 (2024). https://doi.org/10.1007/s11075-023-01709-4

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  • DOI: https://doi.org/10.1007/s11075-023-01709-4

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