Absolute stability region
Stable region in red.

Coefficients

\begin{align} \begin{array}{c|ccccccccccccc} & & & & & & & & & & & & & \\ 0.056 & 0.056 & & & & & & & & & & & & \\ 0.083 & 0.021 & 0.062 & & & & & & & & & & & \\ 0.125 & 0.031 & & 0.094 & & & & & & & & & & \\ 0.312 & 0.312 & & -1.172 & 1.172 & & & & & & & & & \\ 0.375 & 0.037 & & & 0.188 & 0.150 & & & & & & & & \\ 0.148 & 0.048 & & & 0.112 & -0.026 & 0.013 & & & & & & & \\ 0.465 & 0.017 & & & 0.388 & 0.036 & 0.197 & -0.173 & & & & & & \\ 0.565 & 0.069 & & & -0.634 & -0.161 & 0.139 & 0.941 & 0.212 & & & & & \\ 0.650 & 0.184 & & & -2.469 & -0.291 & -0.026 & 2.848 & 0.281 & 0.124 & & & & \\ 0.925 & -1.215 & & & 16.673 & 0.916 & -6.057 & -16.004 & 14.849 & -13.372 & 5.134 & & & \\ 1.000 & 0.259 & & & -4.774 & -0.435 & -3.049 & 5.578 & 6.156 & -5.062 & 2.194 & 0.135 & & \\ 1.000 & 0.822 & & & -11.659 & -0.758 & 0.714 & 12.076 & -2.128 & 1.990 & -0.234 & 0.176 & & \\ \hline & 0.042 & & & & & -0.055 & 0.239 & 0.704 & -0.760 & 0.661 & 0.158 & -0.238 & 0.250\\ & 0.030 & & & & & -0.829 & 0.311 & 2.467 & -2.547 & 1.444 & 0.079 & 0.044 & \end{array}\end{align}

Properties

  • Order of accuracy: $8$
  • Stage order: $1$
  • Stability function: $$1 + z + \frac{z^{2}}{2} + \frac{z^{3}}{6} + \frac{z^{4}}{24} + \frac{z^{5}}{120} + \frac{z^{6}}{720} + \frac{z^{7}}{5040} + \frac{z^{8}}{40320} + 2.75212799010471 \cdot 10^{-6} z^{9} + 2.42319965869587 \cdot 10^{-7} z^{10} + 2.43897182054432 \cdot 10^{-8} z^{11} - 2.03461528968577 \cdot 10^{-10} z^{12}$$
  • Radius of absolute monotonicity: $0$
  • Principal error norm: 4.50744720012e-06
  • Imaginary stability interval: 0.105457557627
  • Real stability interval: 5.16663361997
  • Zero-stable: True