SSPIRK43
Diagonally implicit Runge-Kutta method
Coefficients
\begin{align}
\begin{array}{c|cccc}
- \frac{\sqrt{15}}{10} + \frac{1}{2} & - \frac{\sqrt{15}}{10} + \frac{1}{2} & & & \\
- \frac{\sqrt{15}}{30} + \frac{1}{2} & \frac{\sqrt{15}}{15} & - \frac{\sqrt{15}}{10} + \frac{1}{2} & & \\
\frac{\sqrt{15}}{30} + \frac{1}{2} & \frac{\sqrt{15}}{15} & \frac{\sqrt{15}}{15} & - \frac{\sqrt{15}}{10} + \frac{1}{2} & \\
\frac{\sqrt{15}}{10} + \frac{1}{2} & \frac{\sqrt{15}}{15} & \frac{\sqrt{15}}{15} & \frac{\sqrt{15}}{15} & - \frac{\sqrt{15}}{10} + \frac{1}{2}\\
\hline
& \frac{1}{4} & \frac{1}{4} & \frac{1}{4} & \frac{1}{4}
\end{array}\end{align}
Properties
- Order of accuracy: $3$
- Stage order: $1$
- Stability function: $$\frac{1 + z \left(-1 + \frac{2 \sqrt{15}}{5}\right) + z^{2} \left(\frac{9}{10} - \frac{\sqrt{15}}{5}\right) + z^{3} \left(\frac{1}{6} - \frac{\sqrt{15}}{25}\right) + z^{4} \left(- \frac{67}{300} + \frac{13 \sqrt{15}}{225}\right)}{1 + z \left(-2 + \frac{2 \sqrt{15}}{5}\right) + z^{2} \left(\frac{12}{5} - \frac{3 \sqrt{15}}{5}\right) + z^{3} \left(- \frac{7}{5} + \frac{9 \sqrt{15}}{25}\right) + z^{4} \left(\frac{31}{100} - \frac{2 \sqrt{15}}{25}\right)}$$
- Radius of absolute monotonicity: $6.873$
- Principal error norm: 0.00193249684614
- Zero-stable: True