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:
- Faculty of Physics, Lomonosov Moscow State University
- RUDN University
- Federal Research Center Keldysh Institute of Applied Mathematics, Russian Academy of Sciences
- Issue: Vol 99, No 2 (2019)
- Pages: 230-234
- Section: Computer Science
- URL: https://journals.rcsi.science/1064-5624/article/view/225665
- DOI: https://doi.org/10.1134/S1064562419020273
- ID: 225665
Cite item
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
Faculty of Physics, Lomonosov Moscow State University; RUDN University
Author for correspondence.
Email: aa.belov@physics.msu.ru
Russian Federation, Moscow, 119992; Moscow, 117198
N. N. Kalitkin
Federal Research Center Keldysh Institute of Applied Mathematics, Russian Academy of Sciences
Author for correspondence.
Email: kalitkin@imamod.ru
Russian Federation, Moscow,
125047
P. E. Bulatov
Faculty of Physics, Lomonosov Moscow State University
Email: kalitkin@imamod.ru
Russian Federation, Moscow, 119992
E. K. Zholkovskii
Faculty of Physics, Lomonosov Moscow State University
Email: kalitkin@imamod.ru
Russian Federation, Moscow, 119992