Gauss-Legendre RK36
Implicit Runge-Kutta method
Coefficients
\begin{align}
\begin{array}{c|ccc}
- \frac{\sqrt{15}}{10} + \frac{1}{2} & \frac{5}{36} & - \frac{\sqrt{15}}{15} + \frac{2}{9} & - \frac{\sqrt{15}}{30} + \frac{5}{36}\\
\frac{1}{2} & \frac{5}{36} + \frac{\sqrt{15}}{24} & \frac{2}{9} & - \frac{\sqrt{15}}{24} + \frac{5}{36}\\
\frac{\sqrt{15}}{10} + \frac{1}{2} & \frac{\sqrt{15}}{30} + \frac{5}{36} & \frac{2}{9} + \frac{\sqrt{15}}{15} & \frac{5}{36}\\
\hline
& \frac{5}{18} & \frac{4}{9} & \frac{5}{18}
\end{array}\end{align}
Properties
- Order of accuracy: $6$
- Stage order: $3$
- Stability function: $$\frac{1 + \frac{z}{2} + \frac{z^{2}}{10} + \frac{z^{3}}{120}}{1 - \frac{z}{2} + \frac{z^{2}}{10} - \frac{z^{3}}{120}}$$
- Radius of absolute monotonicity: $0$
- Principal error norm: 0.000165046690524
- Zero-stable: True