Stability Mountain for Runge-Kutta 4

The classical Runge-Kutta method of order 4 with 4 stages. $$ \begin{array}{c|cccc} {1\over2} & {1\over2}\\ {1\over2} & 0 & {1\over2}\\ 1 & 0 & 0 & 1\\ \hline & {1\over6} & {1\over3} & {1\over3} & {1\over6} \end{array} $$ Runge-Kutta formulas can be formulated as multistep methods: $$ \begin{aligned} Y_1 &= y_{n-1}, \\[6pt] Y_2 &= y_{n-1} + \frac{h}{2} f(Y_1), \\[6pt] Y_3 &= y_{n-1} + \frac{h}{2}…