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I have to prepare a task for my Numerical Analysis class in which I compare the performance of RK4 (not A-stable) and BDF2 (A-stable) for the solution of the stiff Van der Poll equation. I've managed to implement both methods in Matlab, however, I can't seem to find a step size and/or value for $\mu$ for which RK4 converges in a weakly stable manner (error grows as $t \to \infty$). Either it completely diverges, or it converges perfectly:

h = 0.071 enter image description here

h = 0.072 enter image description here

I would greatly appreciate any help finding the right step size to display weakly stable behaviour.

Othman El Hammouchi
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    Please define "weakly stable". The central Euler method is weakly stable, but that is a property of the method, not the step size. Van der Pol has fast and slow zones that have different optimal step sizes relative to some desired error level or stability behavior. – Lutz Lehmann Apr 17 '21 at 19:26
  • I mean that I want to find a step size $h$ outside the region of absolute stability, for which RK4 performs fine for some time and then starts oscillating/exploding, much like in the graphic shown here: http://minitorn.tlu.ee/~jaagup/uk/dynsys/ds2/num/Absolute/Absolute.html This is often used to illustrate weak stability. – Othman El Hammouchi Apr 17 '21 at 23:53

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