Absolute stability region
Stable region in red.

Coefficients

\begin{align} \begin{array}{c|ccccccccc} & & & & & & & & & \\ 0.133 & 0.133 & & & & & & & & \\ 0.200 & 0.050 & 0.150 & & & & & & & \\ 0.300 & 0.075 & & 0.225 & & & & & & \\ 0.560 & 0.441 & -1.143 & 0.695 & 0.567 & & & & & \\ 0.760 & -1.904 & 4.317 & 1.068 & -3.937 & 1.216 & & & & \\ 0.987 & 4.831 & -7.633 & -7.401 & 13.165 & -2.682 & 0.707 & & & \\ 1.000 & 6.048 & -9.414 & -9.717 & 16.746 & -3.511 & 0.867 & -0.018 & & \\ 1.000 & 0.061 & & 0.285 & 0.044 & 0.305 & 0.164 & 0.516 & -0.376 & \\ \hline & \frac{17572349}{289262523} & & \frac{57513011}{201864250} & \frac{15587306}{354501571} & \frac{71783021}{234982865} & \frac{29672000}{180480167} & \frac{65567621}{127060952} & - \frac{79074570}{210557597} & \\ & \frac{15231665}{510830334} & & \frac{59452991}{116050448} & - \frac{28398517}{122437738} & \frac{56673824}{137010559} & \frac{68003849}{426673583} & \frac{7097631}{37564021} & - \frac{71226429}{583093742} & \frac{1}{20} \end{array}\end{align}

Properties

  • Order of accuracy: $6$
  • Stage order: $1$
  • Stability function: $$1 + z + \frac{z^{2}}{2} + \frac{z^{3}}{6} + \frac{z^{4}}{24} + \frac{z^{5}}{120} + \frac{z^{6}}{720} + 0.000219397640216706 z^{7} + 1.46573825264896 \cdot 10^{-5} z^{8}$$
  • Radius of absolute monotonicity: $0$
  • Principal error norm: 6.00527264111e-05
  • Imaginary stability interval: 0.016163852379
  • Real stability interval: 4.46337701223
  • Zero-stable: True