Absolute stability region
Stable region in red.

Coefficients

\begin{align} \begin{array}{c|ccc} - \frac{\sqrt{2}}{4} + \frac{1}{2} & - \frac{\sqrt{2}}{4} + \frac{1}{2} & & \\ \frac{1}{2} & \frac{\sqrt{2}}{4} & - \frac{\sqrt{2}}{4} + \frac{1}{2} & \\ \frac{\sqrt{2}}{4} + \frac{1}{2} & \frac{\sqrt{2}}{4} & \frac{\sqrt{2}}{4} & - \frac{\sqrt{2}}{4} + \frac{1}{2}\\ \hline & \frac{1}{3} & \frac{1}{3} & \frac{1}{3} \end{array}\end{align}

Properties

  • Order of accuracy: $3$
  • Stage order: $1$
  • Stability function: $$\frac{1 + z \left(- \frac{1}{2} + \frac{3 \sqrt{2}}{4}\right) + z^{3} \left(\frac{11}{48} - \frac{5 \sqrt{2}}{32}\right) + \frac{z^{2}}{8}}{1 + z \left(- \frac{3}{2} + \frac{3 \sqrt{2}}{4}\right) + z^{2} \left(\frac{9}{8} - \frac{3 \sqrt{2}}{4}\right) + z^{3} \left(- \frac{5}{16} + \frac{7 \sqrt{2}}{32}\right)}$$
  • Radius of absolute monotonicity: $4.828$
  • Principal error norm: 0.00357443490112
  • Zero-stable: True