Issues with positivity-preserving Patankar-type schemes

Patankar-type schemes are linearly implicit time integration methods designed to be unconditionally positivity-preserving. However, there only little results on their stability or robustness. We suggest two approaches analyze the performance and robustness of these methods. In particular, we demonstrate problematic behaviors that, even very simple linear problems, can lead undesired oscillations order reduction for vanishing initial condition. Finally, in numerical simulations that our theoretical problems apply analogously nonlinear stiff problems.