Based on this link, in particular Figure 1, what is the exact meaning of the plot?(adsbygoogle = window.adsbygoogle || []).push({});

To my understanding, it implies that for a given differential equation:

$$ \frac {dy}{dt} = \lambda y $$

that the value ##\lambda \Delta t## has to be within the complex region shown in Figure 1 corresponding to which order of Runge-Kutta you used. To ensure I am understanding this plot correctly, must ##\lambda \Delta t < 0## if both ##\lambda## and ##\Delta t## are purely real? If ##\Delta t## is purely positive and real, wouldn't this restrict you to only considering equations where ##\lambda < 0##?

If we now consider a case where ##\lambda## is complex-valued and ##\Delta t## purely positive and real, what exactly is the intuition behind the value ##\lambda \Delta t = 0.01 + 2i## being stable yet ##\lambda \Delta t = 0.01## not being stable?

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# I Runge-Kutta Stability Regions

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