English: Flame propagation. Top panel shows the solution ${\displaystyle u(t)}$ of the flame propagation problem. Center panel shows stiffness indicator ${\displaystyle F^{\prime }(u)}$. Bottom panel shows reference time scale ${\displaystyle \Delta t(u)}$ (black, logarithmic scale) and step size sequences ${\displaystyle h}$ for an explicit Runge-Kutta method (red, solid line) compared with an implicit A-stable Runge-Kutta method (blue, dashed line), both of third order. In the nonstiff regime (${\displaystyle t<0.5}$) the methods use similar step sizes. In the stiff regime (${\displaystyle t>0.5}$), the explicit method is restricted to using short steps, comparable to the reference time scale, while the implicit method uses step sizes two orders of magnitude larger.