English: Van der Pol equation. Top panel shows solution component ${\displaystyle x}$ of the van der Pol equation for ${\displaystyle \kappa =200}$. Center panel shows the stiffness indicator. It is large and negative during the smooth parts of the solution, where stiffness is proportional to ${\displaystyle {\kappa }^2}$. Bottom panel shows the step size stiffness factor ${\displaystyle h/\mathrm{\Delta }t(u)}$ for four step size sequences produced by an adaptive third order A-stable Runge-Kutta method, for error tolerances ${\displaystyle 10^{-4},10^{-6},10^{-8}}$ and ${\displaystyle 10^{-10}}$. Because the error estimator is of second order, the step size magnitude decreases by one order of magnitude when the tolerance is decreased by two orders. Except for near the unstable transitions, the step sizes are much larger than the reference time scale.