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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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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DOI: https://doi.org/10.1007/s40314-020-01200-z