Explicit Methods for Integrating Stiff Cauchy Problems

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 cor...

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Veröffentlicht in:Doklady. Mathematics 2019-03, Vol.99 (2), p.230-234
Hauptverfasser: Belov, A. A., Kalitkin, N. N., Bulatov, P. E., Zholkovskii, E. K.
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Sprache:eng
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Zusammenfassung: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.
ISSN:1064-5624
1531-8362
DOI:10.1134/S1064562419020273