{title2=$R(z)=1+z+z^2/2+z^3/6+z^4/24$}

= RK4
{c}
{synonym}

The classical four-stage explicit <Runge-Kutta method> uses
$$
A=\begin{pmatrix}0&0&0&0\\1/2&0&0&0\\0&1/2&0&0\\0&0&1&0\end{pmatrix},\qquad
b=(1/6,1/3,1/3,1/6)^T,\qquad c=(0,1/2,1/2,1)^T.
$$
It 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 $|q|\leq2\sqrt2$.


 Classical fourth-order Runge-Kutta method

ID: classical-fourth-order-runge-kutta-method