First-order methodΒΆ
A first-order explicit Runge-Kutta method is nothing else but the Euler-forward scheme:
\[ \begin{align}\begin{aligned}& q^0 = p^n\\& q^1 = p^n + a_{1, 0} f \left( q^0 \right) \Delta t\\& p^{n + 1} = q^1\end{aligned}\end{align} \]
The Butcher tableau is
\[\begin{split}\begin{array}{c|c}
b_0 & a_{0,0} \\
\hline
& a_{1,0} \\
\end{array}
=
\begin{array}{c|c}
0 & 0 \\
\hline
& 1 \\
\end{array}\end{split}\]
This is already a low-storage scheme:
\[\begin{split}\begin{array}{c|c}
k & 0 \\
\hline
\beta^k & 0 \\
\gamma^k & 1
\end{array}\end{split}\]