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Recent Developments in the Field of Modified Patankar-Runge-Kutta-methods

Izgin, Thomas
Kopecz, Stefan
Meister, Andreas

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.

Sponsor
Gefördert im Rahmen des Projekts DEAL
Citation
In: Proceedings in applied mathematics and mechanics (PAMM) Volume 21 / Issue 1 (2021-12-14) , S. ; eissn:1617-7061
Collections
@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},
  keywords ={510 and Runge-Kutta-Verfahren and Entwicklung and Numerische Mathematik},
  copyright  ={http://creativecommons.org/licenses/by-nc/4.0/},
  language ={en},
  journal  ={Proceedings in applied mathematics and mechanics (PAMM)},
  year   ={2021-12-14}
}