Absolute stability region
Stable region in red.

Coefficients

\begin{align} \begin{array}{c|ccccccccc} & & & & & & & & & \\ \frac{1}{6} & \frac{1}{6} & & & & & & & & \\ \frac{1}{3} & \frac{1}{6} & \frac{1}{6} & & & & & & & \\ \frac{1}{2} & \frac{1}{6} & \frac{1}{6} & \frac{1}{6} & & & & & & \\ \frac{2}{3} & \frac{1}{6} & \frac{1}{6} & \frac{1}{6} & \frac{1}{6} & & & & & \\ \frac{5}{6} & \frac{1}{6} & \frac{1}{6} & \frac{1}{6} & \frac{1}{6} & \frac{1}{6} & & & & \\ \frac{1}{2} & \frac{1}{6} & \frac{1}{15} & \frac{1}{15} & \frac{1}{15} & \frac{1}{15} & \frac{1}{15} & & & \\ \frac{2}{3} & \frac{1}{6} & \frac{1}{15} & \frac{1}{15} & \frac{1}{15} & \frac{1}{15} & \frac{1}{15} & \frac{1}{6} & & \\ \frac{5}{6} & \frac{1}{6} & \frac{1}{15} & \frac{1}{15} & \frac{1}{15} & \frac{1}{15} & \frac{1}{15} & \frac{1}{6} & \frac{1}{6} & \\ \hline & \frac{1}{6} & \frac{1}{15} & \frac{1}{15} & \frac{1}{15} & \frac{1}{15} & \frac{1}{15} & \frac{1}{6} & \frac{1}{6} & \frac{1}{6} \end{array}\end{align}

Properties

  • Order of accuracy: $3$
  • Stage order: $1$
  • Stability function: $$1 + z + \frac{z^{2}}{2} + \frac{z^{3}}{6} + \frac{17 z^{4}}{432} + \frac{7 z^{5}}{1080} + \frac{7 z^{6}}{9720} + \frac{z^{7}}{19440} + \frac{z^{8}}{466560} + \frac{z^{9}}{25194240}$$
  • Radius of absolute monotonicity: $6.000$
  • Principal error norm: 0.00896523922733
  • Imaginary stability interval: 4.11764802562
  • Real stability interval: 13.2897595067
  • Zero-stable: True