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

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 ch...

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Bibliographic Details
Published inProceedings in applied mathematics and mechanics Vol. 21; no. 1
Main Authors Izgin, Thomas, Kopecz, Stefan, Meister, Andreas
Format Journal Article
LanguageEnglish
Published Berlin Wiley-VCH GmbH 01.12.2021
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Summary: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.
ISSN:1617-7061
1617-7061
DOI:10.1002/pamm.202100027