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Explicit Methods for Integrating Stiff Cauchy Problems

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Abstract

An explicit method for solving stiff Cauchy problems is proposed. The method relies on explicit schemes and a step size selection algorithm based on the curvature of an integral curve. Closed-form formulas are derived for finding the curvature. For Runge–Kutta schemes with up to four stages, the corresponding sets of coefficients are given. The method is validated on a test problem with a given exact solution. It is shown that the method is as accurate and robust as implicit methods, but is substantially superior to them in efficiency. A numerical example involving chemical kinetics computations with 9 components and 50 reactions is given.

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ACKNOWLEDGMENTS

This work was supported by the Russian Foundation for Basic Research, project no. 18-01-00175 and by the RUDN 5-100 program.

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Authors and Affiliations

  1. Faculty of Physics, Lomonosov Moscow State University, 119992, Moscow, Russia

    A. A. Belov, P. E. Bulatov & E. K. Zholkovskii

  2. RUDN University, 117198, Moscow, Russia

    A. A. Belov

  3. Federal Research Center Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, 125047, Moscow, Russia

    N. N. Kalitkin

Authors
  1. A. A. Belov
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  2. N. N. Kalitkin
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  3. P. E. Bulatov
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  4. E. K. Zholkovskii
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Corresponding authors

Correspondence to A. A. Belov or N. N. Kalitkin.

Additional information

Translated by I. Ruzanova

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Belov, A.A., Kalitkin, N.N., Bulatov, P.E. et al. Explicit Methods for Integrating Stiff Cauchy Problems. Dokl. Math. 99, 230–234 (2019). https://doi.org/10.1134/S1064562419020273

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  • DOI: https://doi.org/10.1134/S1064562419020273

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