On the stability of strong-stability-preserving modified Patankar Runge-Kutta schemes

TL;DR

This paper analyzes the stability of second and third order SSPMPRK schemes for convection equations with stiff sources, identifying parameter ranges for stability and validating findings through numerical experiments.

Contribution

It provides a stability analysis for SSPMPRK schemes, revealing parameter conditions for stability and demonstrating their effectiveness with numerical tests.

Findings

Parameter ranges for stability identified

Numerical experiments confirm theoretical analysis

Schemes maintain positivity under CFL condition

Abstract

In this paper, we perform stability analysis for a class of second and third order accurate strong-stability-preserving modified Patankar Runge-Kutta (SSPMPRK) schemes, which were introduced in [4,5] 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.