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.

翻译：在本文中,我们对第二和第三等级的精密坚固保全系统进行了稳定性分析,在[4,5] 中引入了经修改的Patankar Runge-Kutta(SSPMPRK)方案,可用于用严格的源词解决对流方程,如反应式Euler方程,根据标准的CFL条件,仅由于对流术语而保证有相对性。分析使我们能够确定这些SSPMPRK方案的自由参数范围,以确保稳定性。提供了数字实验,以证明分析的有效性。