Absolute stability region
Stable region in red.

Coefficients

\begin{align} \begin{array}{c|cccccccccc} & & & & & & & & & & \\ \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{1}{3} & \frac{1}{15} & \frac{1}{15} & \frac{1}{15} & \frac{1}{15} & \frac{1}{15} & & & & & \\ \frac{1}{2} & \frac{1}{15} & \frac{1}{15} & \frac{1}{15} & \frac{1}{15} & \frac{1}{15} & \frac{1}{6} & & & & \\ \frac{2}{3} & \frac{1}{15} & \frac{1}{15} & \frac{1}{15} & \frac{1}{15} & \frac{1}{15} & \frac{1}{6} & \frac{1}{6} & & & \\ \frac{5}{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} & & \\ 1 & \frac{1}{15} & \frac{1}{15} & \frac{1}{15} & \frac{1}{15} & \frac{1}{15} & \frac{1}{6} & \frac{1}{6} & \frac{1}{6} & \frac{1}{6} & \\ \hline & \frac{1}{10} & \frac{1}{10} & \frac{1}{10} & \frac{1}{10} & \frac{1}{10} & \frac{1}{10} & \frac{1}{10} & \frac{1}{10} & \frac{1}{10} & \frac{1}{10} \end{array}\end{align}

Properties

  • Order of accuracy: $4$
  • Stage order: $1$
  • Stability function: $$1 + z + \frac{z^{2}}{2} + \frac{z^{3}}{6} + \frac{z^{4}}{24} + \frac{17 z^{5}}{2160} + \frac{7 z^{6}}{6480} + \frac{z^{7}}{9720} + \frac{z^{8}}{155520} + \frac{z^{9}}{4199040} + \frac{z^{10}}{251942400}$$
  • Radius of absolute monotonicity: $6.000$
  • Principal error norm: 0.00221122374705
  • Imaginary stability interval: 4.92145307073
  • Real stability interval: 13.9170474646
  • Zero-stable: True