Radau IIA3

Absolute stability region — Stable region in red.

Coefficients

$\begin{align} \begin{array}{c|ccc} - \frac{\sqrt{6}}{10} + \frac{2}{5} & - \frac{7 \sqrt{6}}{360} + \frac{11}{45} & - \frac{169 \sqrt{6}}{1800} + \frac{37}{225} & - \frac{2}{225} + \frac{\sqrt{6}}{75}\\ \frac{\sqrt{6}}{10} + \frac{2}{5} & \frac{37}{225} + \frac{169 \sqrt{6}}{1800} & \frac{7 \sqrt{6}}{360} + \frac{11}{45} & - \frac{\sqrt{6}}{75} - \frac{2}{225}\\ 1 & - \frac{\sqrt{6}}{36} + \frac{4}{9} & \frac{\sqrt{6}}{36} + \frac{4}{9} & \frac{1}{9}\\ \hline & - \frac{\sqrt{6}}{36} + \frac{4}{9} & \frac{\sqrt{6}}{36} + \frac{4}{9} & \frac{1}{9} \end{array}\end{align}$

Properties

Order of accuracy: $5$
Stage order: $3$
Stability function: $\frac{1 + \frac{2 z}{5} + \frac{z^{2}}{20}}{1 - \frac{3 z}{5} + \frac{3 z^{2}}{20} - \frac{z^{3}}{60}}$
Radius of absolute monotonicity: $0$
Principal error norm: 0.000989528507253
Zero-stable: True