Runge-Kutta-Chebyshev (20,1)
Explicit Runge-Kutta method
Coefficients
\begin{align}
\begin{array}{c|cccccccccccccccccccc}
& & & & & & & & & & & & & & & & & & & & \\
\frac{1}{400} & \frac{1}{400} & & & & & & & & & & & & & & & & & & & \\
\frac{1}{100} & \frac{1}{200} & \frac{1}{200} & & & & & & & & & & & & & & & & & & \\
\frac{9}{400} & \frac{3}{400} & \frac{1}{100} & \frac{1}{200} & & & & & & & & & & & & & & & & & \\
\frac{1}{25} & \frac{1}{100} & \frac{3}{200} & \frac{1}{100} & \frac{1}{200} & & & & & & & & & & & & & & & & \\
\frac{1}{16} & \frac{1}{80} & \frac{1}{50} & \frac{3}{200} & \frac{1}{100} & \frac{1}{200} & & & & & & & & & & & & & & & \\
\frac{9}{100} & \frac{3}{200} & \frac{1}{40} & \frac{1}{50} & \frac{3}{200} & \frac{1}{100} & \frac{1}{200} & & & & & & & & & & & & & & \\
\frac{49}{400} & \frac{7}{400} & \frac{3}{100} & \frac{1}{40} & \frac{1}{50} & \frac{3}{200} & \frac{1}{100} & \frac{1}{200} & & & & & & & & & & & & & \\
\frac{4}{25} & \frac{1}{50} & \frac{7}{200} & \frac{3}{100} & \frac{1}{40} & \frac{1}{50} & \frac{3}{200} & \frac{1}{100} & \frac{1}{200} & & & & & & & & & & & & \\
\frac{81}{400} & \frac{9}{400} & \frac{1}{25} & \frac{7}{200} & \frac{3}{100} & \frac{1}{40} & \frac{1}{50} & \frac{3}{200} & \frac{1}{100} & \frac{1}{200} & & & & & & & & & & & \\
\frac{1}{4} & \frac{1}{40} & \frac{9}{200} & \frac{1}{25} & \frac{7}{200} & \frac{3}{100} & \frac{1}{40} & \frac{1}{50} & \frac{3}{200} & \frac{1}{100} & \frac{1}{200} & & & & & & & & & & \\
\frac{121}{400} & \frac{11}{400} & \frac{1}{20} & \frac{9}{200} & \frac{1}{25} & \frac{7}{200} & \frac{3}{100} & \frac{1}{40} & \frac{1}{50} & \frac{3}{200} & \frac{1}{100} & \frac{1}{200} & & & & & & & & & \\
\frac{9}{25} & \frac{3}{100} & \frac{11}{200} & \frac{1}{20} & \frac{9}{200} & \frac{1}{25} & \frac{7}{200} & \frac{3}{100} & \frac{1}{40} & \frac{1}{50} & \frac{3}{200} & \frac{1}{100} & \frac{1}{200} & & & & & & & & \\
\frac{169}{400} & \frac{13}{400} & \frac{3}{50} & \frac{11}{200} & \frac{1}{20} & \frac{9}{200} & \frac{1}{25} & \frac{7}{200} & \frac{3}{100} & \frac{1}{40} & \frac{1}{50} & \frac{3}{200} & \frac{1}{100} & \frac{1}{200} & & & & & & & \\
\frac{49}{100} & \frac{7}{200} & \frac{13}{200} & \frac{3}{50} & \frac{11}{200} & \frac{1}{20} & \frac{9}{200} & \frac{1}{25} & \frac{7}{200} & \frac{3}{100} & \frac{1}{40} & \frac{1}{50} & \frac{3}{200} & \frac{1}{100} & \frac{1}{200} & & & & & & \\
\frac{9}{16} & \frac{3}{80} & \frac{7}{100} & \frac{13}{200} & \frac{3}{50} & \frac{11}{200} & \frac{1}{20} & \frac{9}{200} & \frac{1}{25} & \frac{7}{200} & \frac{3}{100} & \frac{1}{40} & \frac{1}{50} & \frac{3}{200} & \frac{1}{100} & \frac{1}{200} & & & & & \\
\frac{16}{25} & \frac{1}{25} & \frac{3}{40} & \frac{7}{100} & \frac{13}{200} & \frac{3}{50} & \frac{11}{200} & \frac{1}{20} & \frac{9}{200} & \frac{1}{25} & \frac{7}{200} & \frac{3}{100} & \frac{1}{40} & \frac{1}{50} & \frac{3}{200} & \frac{1}{100} & \frac{1}{200} & & & & \\
\frac{289}{400} & \frac{17}{400} & \frac{2}{25} & \frac{3}{40} & \frac{7}{100} & \frac{13}{200} & \frac{3}{50} & \frac{11}{200} & \frac{1}{20} & \frac{9}{200} & \frac{1}{25} & \frac{7}{200} & \frac{3}{100} & \frac{1}{40} & \frac{1}{50} & \frac{3}{200} & \frac{1}{100} & \frac{1}{200} & & & \\
\frac{81}{100} & \frac{9}{200} & \frac{17}{200} & \frac{2}{25} & \frac{3}{40} & \frac{7}{100} & \frac{13}{200} & \frac{3}{50} & \frac{11}{200} & \frac{1}{20} & \frac{9}{200} & \frac{1}{25} & \frac{7}{200} & \frac{3}{100} & \frac{1}{40} & \frac{1}{50} & \frac{3}{200} & \frac{1}{100} & \frac{1}{200} & & \\
\frac{361}{400} & \frac{19}{400} & \frac{9}{100} & \frac{17}{200} & \frac{2}{25} & \frac{3}{40} & \frac{7}{100} & \frac{13}{200} & \frac{3}{50} & \frac{11}{200} & \frac{1}{20} & \frac{9}{200} & \frac{1}{25} & \frac{7}{200} & \frac{3}{100} & \frac{1}{40} & \frac{1}{50} & \frac{3}{200} & \frac{1}{100} & \frac{1}{200} & \\
\hline
& \frac{1}{20} & \frac{19}{200} & \frac{9}{100} & \frac{17}{200} & \frac{2}{25} & \frac{3}{40} & \frac{7}{100} & \frac{13}{200} & \frac{3}{50} & \frac{11}{200} & \frac{1}{20} & \frac{9}{200} & \frac{1}{25} & \frac{7}{200} & \frac{3}{100} & \frac{1}{40} & \frac{1}{50} & \frac{3}{200} & \frac{1}{100} & \frac{1}{200}
\end{array}\end{align}
Properties
- Order of accuracy: $1$
- Stage order: $1$
- Stability function: $$1 + z + \frac{133 z^{2}}{800} + \frac{4389 z^{3}}{400000} + \frac{245157 z^{4}}{640000000} + \frac{81719 z^{5}}{10000000000} + \frac{7429 z^{6}}{64000000000} + \frac{7429 z^{7}}{6400000000000} + \frac{869193 z^{8}}{102400000000000000} + \frac{119301 z^{9}}{2560000000000000000} + \frac{2003001 z^{10}}{10240000000000000000000} + \frac{26013 z^{11}}{40960000000000000000000} + \frac{105183 z^{12}}{65536000000000000000000000} + \frac{8091 z^{13}}{2560000000000000000000000000} + \frac{9889 z^{14}}{2048000000000000000000000000000} + \frac{5797 z^{15}}{1024000000000000000000000000000000} + \frac{1309 z^{16}}{262144000000000000000000000000000000} + \frac{z^{17}}{355687428096000} + \frac{z^{18}}{6402373705728000} + \frac{z^{19}}{121645100408832000} + \frac{z^{20}}{2432902008176640000}$$
- Radius of absolute monotonicity: $1.233$
- Principal error norm: 0.33375
- Imaginary stability interval: 0
- Real stability interval: 76.3931005316
- Zero-stable: True