SSPRK(10,4)

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