Aufsatz
Recent Developments in the Field of Modified Patankar-Runge-Kutta-methods
Zusammenfassung
Modified Patankar-Runge-Kutta (MPRK) schemes are numerical one-step methods for the solution of positive and conservative production-destruction systems (PDS). They adapt explicit Runge-Kutta schemes in a way to ensure positivity and conservation of the numerical approximation irrespective of the chosen time step size. Due to nonlinear relationships between the next and current iterate, the stability analysis for such schemes is lacking. In this work, we introduce a strategy to analyze the MPRK22(α)-schemes in the case of positive and conservative PDS. Thereby, we point out that a usual stability analysis based on Dahlquist's equation is not possible in order to understand the properties of this class of schemes.
Zitierform
In: Proceedings in applied mathematics and mechanics (PAMM) Volume 21 / Issue 1 (2021-12-14) eissn:1617-7061Förderhinweis
Gefördert im Rahmen des Projekts DEALZitieren
@article{doi:10.17170/kobra-202112165265,
author={Izgin, Thomas and Kopecz, Stefan and Meister, Andreas},
title={Recent Developments in the Field of Modified Patankar-Runge-Kutta-methods},
journal={Proceedings in applied mathematics and mechanics (PAMM)},
year={2021}
}
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2022-02-15T16:41:33Z 2022-02-15T16:41:33Z 2021-12-14 doi:10.17170/kobra-202112165265 http://hdl.handle.net/123456789/13622 Gefördert im Rahmen des Projekts DEAL eng Namensnennung-Nicht-kommerziell 4.0 International http://creativecommons.org/licenses/by-nc/4.0/ 510 Recent Developments in the Field of Modified Patankar-Runge-Kutta-methods Aufsatz Modified Patankar-Runge-Kutta (MPRK) schemes are numerical one-step methods for the solution of positive and conservative production-destruction systems (PDS). They adapt explicit Runge-Kutta schemes in a way to ensure positivity and conservation of the numerical approximation irrespective of the chosen time step size. Due to nonlinear relationships between the next and current iterate, the stability analysis for such schemes is lacking. In this work, we introduce a strategy to analyze the MPRK22(α)-schemes in the case of positive and conservative PDS. Thereby, we point out that a usual stability analysis based on Dahlquist's equation is not possible in order to understand the properties of this class of schemes. open access Izgin, Thomas Kopecz, Stefan Meister, Andreas doi:10.1002/pamm.202100027 Runge-Kutta-Verfahren Entwicklung Numerische Mathematik publishedVersion eissn:1617-7061 Issue 1 Proceedings in applied mathematics and mechanics (PAMM) Volume 21 false e202100027
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