Rubin's 4-th Order Method is Neither A-stable Nor D-stable

This is in continuation of: Stability Regions for BDF and Tendler's Formulas Stability Regions for Tischer's Formulas We analyze below method from Rubin , see his Fig. 4.2. Also see Weitere zyklische und blockimplizite lineare Mehrschritt-Verfahren . $$ \begin{array}{r|rr} p=4 && 1 & 2\cr%R4A \hline -1 && 0 & 56\cr 0 && 24 & -72\cr 1 && -24 & 0\cr 2 && 0 & 16\cr \hline -1 && 1 & -21\cr 0 && -13 &…