Coefficients
\begin{align}
\begin{array}{c|ccccccccccccccccc}
& & & & & & & & & & & & & & & & & \\
\frac{1}{2} & \frac{1}{2} & & & & & & & & & & & & & & & & \\
\frac{1}{4} & \frac{1}{4} & & & & & & & & & & & & & & & & \\
\frac{1}{2} & & & \frac{1}{2} & & & & & & & & & & & & & & \\
\frac{3}{4} & \frac{1}{4} & & & \frac{1}{2} & & & & & & & & & & & & & \\
\frac{1}{6} & \frac{1}{6} & & & & & & & & & & & & & & & & \\
\frac{1}{3} & & & & & & \frac{1}{3} & & & & & & & & & & & \\
\frac{1}{2} & \frac{1}{6} & & & & & & \frac{1}{3} & & & & & & & & & & \\
\frac{2}{3} & & & & & & \frac{1}{3} & & \frac{1}{3} & & & & & & & & & \\
\frac{5}{6} & \frac{1}{6} & & & & & & \frac{1}{3} & & \frac{1}{3} & & & & & & & & \\
\frac{1}{8} & \frac{1}{8} & & & & & & & & & & & & & & & & \\
\frac{1}{4} & & & & & & & & & & & \frac{1}{4} & & & & & & \\
\frac{3}{8} & \frac{1}{8} & & & & & & & & & & & \frac{1}{4} & & & & & \\
\frac{1}{2} & & & & & & & & & & & \frac{1}{4} & & \frac{1}{4} & & & & \\
\frac{5}{8} & \frac{1}{8} & & & & & & & & & & & \frac{1}{4} & & \frac{1}{4} & & & \\
\frac{3}{4} & & & & & & & & & & & \frac{1}{4} & & \frac{1}{4} & & \frac{1}{4} & & \\
\frac{7}{8} & \frac{1}{8} & & & & & & & & & & & \frac{1}{4} & & \frac{1}{4} & & \frac{1}{4} & \\
\hline
& & - \frac{1}{360} & \frac{8}{45} & & \frac{8}{45} & - \frac{243}{280} & & - \frac{243}{280} & & - \frac{243}{280} & \frac{256}{315} & & \frac{256}{315} & & \frac{256}{315} & & \frac{256}{315}\\
& & & \frac{2}{15} & & \frac{2}{15} & - \frac{27}{35} & & - \frac{27}{35} & & - \frac{27}{35} & \frac{16}{21} & & \frac{16}{21} & & \frac{16}{21} & & \frac{16}{21}
\end{array}\end{align}
Properties
-
Order of accuracy: $8$
-
Stage order: $1$
-
Stability function: $$1 + z + \frac{z^{2}}{2} + \frac{z^{3}}{6} + \frac{z^{4}}{24} + \frac{z^{5}}{120} + \frac{z^{6}}{720} + \frac{z^{7}}{5040} + \frac{z^{8}}{40320}$$
-
Radius of absolute monotonicity: $0$
- Principal error norm: 3.02658988366e-05
- Imaginary stability interval: 3.39514022057
- Real stability interval: 4.31362722777
- Zero-stable: True