Classical fourth-order Runge-Kutta method ($R(z)=1+z+z^2/2+z^3/6+z^4/24$)

The classical four-stage explicit Runge-Kutta method usesIt satisfies the fourth-order conditions for a Runge-Kutta method. Its polynomial stability function excludes A-stability, while $|R(iq){|}^2=1-q^6/72+q^8/576$ gives the imaginary-axis stability interval $|q|\le 2\sqrt{2}$.