Stability domains as defined in Eq. (10) of the schemes involved in PIROCK: ROCK2 (in gray. here s = 13 internal stages) for diffusion terms, an explicit method of order 3 for advection terms (dark gray), and the L-stable diagonally implicit Runge–Kutta method of order 2 for stiff reaction terms (light gray). Right picture: Zoom near the origin to illustrate that the advection method (dark gray) includes the portion of the imaginary axis. The stability domains are plotted for z in the complex plane (horizontal axis: real part Re(z), vertical axis: imaginary part Im(z)).