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