Article | Proceedings of The 9th EUROSIM Congress on Modelling and Simulation, EUROSIM 2016, The 57th SIMS Conference on Simulation and Modelling SIMS 2016 | Solving Stiff Systems of ODEs by Explicit Methods with Conformed Stability Domains Linköping University Electronic Press Conference Proceedings
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Title:
Solving Stiff Systems of ODEs by Explicit Methods with Conformed Stability Domains
Author:
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
DOI:
10.3384/ecp17142973
Download:
Full text (pdf)
Year:
2018
Conference:
Proceedings of The 9th EUROSIM Congress on Modelling and Simulation, EUROSIM 2016, The 57th SIMS Conference on Simulation and Modelling SIMS 2016
Issue:
142
Article no.:
143
Pages:
973-978
No. of pages:
6
Publication type:
Abstract and Fulltext
Published:
2018-12-19
ISBN:
978-91-7685-399-3
Series:
Linköping Electronic Conference Proceedings
ISSN (print):
1650-3686
ISSN (online):
1650-3740
Publisher:
Linköping University Electronic Press, Linköpings universitet


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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

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

Author:
Anton E. Novikov, Mikhail V. Rybkov, Yury V. Shornikov, Lyudmila V. Knaub
Title:
Solving Stiff Systems of ODEs by Explicit Methods with Conformed Stability Domains
DOI:
http://dx.doi.org/10.3384/ecp17142973
References:
No references available

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

Author:
Anton E. Novikov, Mikhail V. Rybkov, Yury V. Shornikov, Lyudmila V. Knaub
Title:
Solving Stiff Systems of ODEs by Explicit Methods with Conformed Stability Domains
DOI:
https://doi.org10.3384/ecp17142973
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