Conference article

Solving Stiff Systems of ODEs by Explicit Methods with Conformed Stability Domains

Anton E. Novikov
Institute of Mathematics and Fundamental Informatics, Siberian Federal University, Russia

Mikhail V. Rybkov
Institute of Mathematics and Fundamental Informatics, Siberian Federal University, Russia

Yury V. Shornikov
Automation and Computer Engineering Department, Novosibirsk State Technical University

Lyudmila V. Knaub
Institute of Mathematics and Fundamental Informatics, Siberian Federal University, Russia

Download articlehttp://dx.doi.org/10.3384/ecp17142973

Published in: Proceedings of The 9th EUROSIM Congress on Modelling and Simulation, EUROSIM 2016, The 57th SIMS Conference on Simulation and Modelling SIMS 2016

Linköping Electronic Conference Proceedings 142:143, p. 973-978

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Published: 2018-12-19

ISBN: 978-91-7685-399-3

ISSN: 1650-3686 (print), 1650-3740 (online)

Abstract

The Cauchy problem for a stiff system of ODEs is considered. The explicit m-stage first order methods of the Runge-Kutta type are designed with stability domains of intermediate numerical schemes conformed with the stability domain of the basic scheme. Inequalities for accuracy and stability control are obtained. A numerical algorithm based on the first-order method and the five-stage fourth order Merson method is developed. The algorithm is aimed at solving large-scale systems of ODEs of moderate stiffness with low accuracy. It has been included in the library of solvers of the ISMA simulation environment. Numerical results showing growth of the efficiency are given.

Keywords

Runge-Kutta methods, accuracy and stability control, conformed stability domains, stiff problems

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