Email this article Explicit methods for integrating stiff Cauchy problems
- Authors: Belov A.A.1,2, Kalitkin N.N.3, Bulatov P.E.1, Zholkovskii E.K.1
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Affiliations:
- Lomonosov Moscow State University
- Peoples Friendship University of Russia
- Institute for Applied Mathematics of the Russian Academy of Sciences
- Issue: Vol 485, No 5 (2019)
- Pages: 553-557
- Section: Informatics
- URL: https://journals.eco-vector.com/0869-5652/article/view/14294
- DOI: https://doi.org/10.31857/S0869-56524855553-557
- ID: 14294
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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.
About the authors
A. A. Belov
Lomonosov Moscow State University; Peoples Friendship University of Russia
Author for correspondence.
Email: aa.belov@physics.msu.ru
Russian Federation, 1, Leninskie gory, Moscow, 119991; 6, Miklukho-Maklaya street, Moscow, 117198
N. N. Kalitkin
Institute for Applied Mathematics of the Russian Academy of Sciences
Email: kalitkin@imamod.ru
Corresponding Member of the Russian Academy of Sciences
Russian Federation, 4, Miusskaya square, Moscow, 125047P. E. Bulatov
Lomonosov Moscow State University
Email: aa.belov@physics.msu.ru
Russian Federation, 1, Leninskie gory, Moscow, 119991
E. K. Zholkovskii
Lomonosov Moscow State University
Email: aa.belov@physics.msu.ru
Russian Federation, 1, Leninskie gory, Moscow, 119991
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