Runge-Kutta-Chebyshev (5,1)
Explicit Runge-Kutta method
Coefficients
\begin{align}
\begin{array}{c|ccccc}
& & & & & \\
\frac{1}{25} & \frac{1}{25} & & & & \\
\frac{4}{25} & \frac{2}{25} & \frac{2}{25} & & & \\
\frac{9}{25} & \frac{3}{25} & \frac{4}{25} & \frac{2}{25} & & \\
\frac{16}{25} & \frac{4}{25} & \frac{6}{25} & \frac{4}{25} & \frac{2}{25} & \\
\hline
& \frac{1}{5} & \frac{8}{25} & \frac{6}{25} & \frac{4}{25} & \frac{2}{25}
\end{array}\end{align}
Properties
- Order of accuracy: $1$
- Stage order: $1$
- Stability function: $$1 + z + \frac{4 z^{2}}{25} + \frac{28 z^{3}}{3125} + \frac{16 z^{4}}{78125} + \frac{16 z^{5}}{9765625}$$
- Radius of absolute monotonicity: $1.224$
- Principal error norm: 0.34
- Imaginary stability interval: 0
- Real stability interval: 45.2254240784
- Zero-stable: True