论文标题
关于强稳定性改良的Patankar Runge-Kutta方案的稳定性
On the stability of strong-stability-preserving modified Patankar Runge-Kutta schemes
论文作者
论文摘要
在本文中，我们对一类二阶和三阶准确稳定稳定性的修改后的Patankar runge-kutta（SSPMPRK）方案进行稳定分析，这些方案在[4,5]中引入，可用于求解具有反应性EULER方程的僵硬对流方程，例如在反应性EULER方程中，仅在适应标准的cffl条件下进行保证。该分析使我们能够确定这些SSPMPRK方案中的自由参数范围，以确保稳定性。提供数值实验以证明分析的有效性。
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.
