Gauss-Legendre RK24
Implicit Runge-Kutta method
Coefficients
\begin{align}
\begin{array}{c|cc}
- \frac{\sqrt{3}}{6} + \frac{1}{2} & \frac{1}{4} & - \frac{\sqrt{3}}{6} + \frac{1}{4}\\
\frac{\sqrt{3}}{6} + \frac{1}{2} & \frac{1}{4} + \frac{\sqrt{3}}{6} & \frac{1}{4}\\
\hline
& \frac{1}{2} & \frac{1}{2}
\end{array}\end{align}
Properties
- Order of accuracy: $4$
- Stage order: $2$
- Stability function: $$\frac{1 + \frac{z}{2} + \frac{z^{2}}{12}}{1 - \frac{z}{2} + \frac{z^{2}}{12}}$$
- Radius of absolute monotonicity: $0$
- Principal error norm: 0.00433062197543
- Zero-stable: True