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Jacobian-dependent vs Jacobian-free discretizations for nonlinear differential problems

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Abstract

The paper provides a comparison between two relevant classes of numerical discretizations for stiff and nonstiff problems. Such a comparison regards linearly implicit Jacobian-dependent Runge–Kutta methods and fully implicit Runge–Kutta methods based on Gauss–Legendre nodes, both A-stable. We show that Jacobian-dependent discretizations are more efficient than Jacobian-free fully implicit methods, as visible in the numerical evidence.

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Acknowledgements

The authors Conte, D’Ambrosio and Paternoster are members of the GNCS group. This work is supported by GNCS-INDAM project and by PRIN2017-MIUR project. The authors thank Prof. Liviu Gr. Ixaru for the precious discussions that inspired this research. The authors are thankful to the anonymous referees for their gifted suggestions.

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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

  2. Department of Information Engineering and Computer Science and Mathematics, University of L’Aquila, Via Vetoio, Loc. Coppito, 67100, L’Aquila, Italy

    Raffaele D’Ambrosio

Authors
  1. Dajana Conte
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  2. Raffaele D’Ambrosio
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  3. Giovanni Pagano
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  4. Beatrice Paternoster
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Correspondence to Raffaele D’Ambrosio.

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Communicated by Jose Alberto Cuminato.

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Conte, D., D’Ambrosio, R., Pagano, G. et al. Jacobian-dependent vs Jacobian-free discretizations for nonlinear differential problems. Comp. Appl. Math. 39, 171 (2020). https://doi.org/10.1007/s40314-020-01200-z

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