Volume 57, Number 2, March-April 2023
|Page(s)||1063 - 1086|
|Published online||12 April 2023|
On the stability of strong-stability-preserving modified Patankar–Runge–Kutta schemes
Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409, USA
2 Department of Mathematics, University of Kassel, Kassel, Hesse, Germany
3 Division of Applied Mathematics, Brown University, Providence, RI 02912, USA
* Corresponding author: email@example.com
Accepted: 9 January 2023
In this paper, we perform a stability analysis for classes of second and third order accurate strong-stability-preserving modified Patankar–Runge–Kutta (SSPMPRK) schemes, which were introduced in Huang and Shu [J. Sci. Comput. 78 (2019) 1811–1839] and Huang et al. [J. Sci. Comput. 79 (2019) 1015–1056] and can be used to solve convection equations with stiff source terms, such as reactive Euler equations, with guaranteed positivity under the standard CFL condition due to the convection terms only. The analysis allows us to identify the range of free parameters in these SSPMPRK schemes in order to ensure stability. Numerical experiments are provided to demonstrate the validity of the analysis.
Mathematics Subject Classification: 65L05 / 65L06 / 65L20
Key words: Stability / strong-stability-preserving / modified Patankar–Runge–Kutta schemes / positivity-preserving
© The authors. Published by EDP Sciences, SMAI 2023
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