Radau-II Runge-Kutta Methods

Radau IIA

Runge-Kutta Tableau RadauIIA(2) with 2 stages and order 3:

\[\begin{array}{r|rr} \frac{1}{3} & \frac{5}{12} & - \frac{1}{12} \\ 1 & \frac{3}{4} & \frac{1}{4} \\\hline & \frac{3}{4} & \frac{1}{4} \\ \end{array}\]

Runge-Kutta Tableau RadauIIA(3) with 3 stages and order 5:

\[\begin{array}{r|rrr} \frac{2}{5} - \frac{\sqrt{6}}{10} & \frac{11}{45} - \frac{7 \sqrt{6}}{360} & \frac{37}{225} - \frac{169 \sqrt{6}}{1800} & - \frac{2}{225} + \frac{\sqrt{6}}{75} \\ \frac{\sqrt{6}}{10} + \frac{2}{5} & \frac{37}{225} + \frac{169 \sqrt{6}}{1800} & \frac{7 \sqrt{6}}{360} + \frac{11}{45} & - \frac{\sqrt{6}}{75} - \frac{2}{225} \\ 1 & \frac{4}{9} - \frac{\sqrt{6}}{36} & \frac{\sqrt{6}}{36} + \frac{4}{9} & \frac{1}{9} \\\hline & \frac{4}{9} - \frac{\sqrt{6}}{36} & \frac{\sqrt{6}}{36} + \frac{4}{9} & \frac{1}{9} \\ \end{array}\]

Radau IIB

Runge-Kutta Tableau RadauIIB(2) with 2 stages and order 3:

\[\begin{array}{r|rr} \frac{1}{3} & \frac{1}{3} & 0 \\ 1 & 1 & 0 \\\hline & \frac{3}{4} & \frac{1}{4} \\ \end{array}\]

Runge-Kutta Tableau RadauIIB(3) with 3 stages and order 5:

\[\begin{array}{r|rrr} \frac{2}{5} - \frac{\sqrt{6}}{10} & \frac{1}{5} - \frac{\sqrt{6}}{120} & \frac{1}{5} - \frac{11 \sqrt{6}}{120} & 0 \\ \frac{\sqrt{6}}{10} + \frac{2}{5} & \frac{1}{5} + \frac{11 \sqrt{6}}{120} & \frac{\sqrt{6}}{120} + \frac{1}{5} & 0 \\ 1 & \frac{1}{2} - \frac{\sqrt{6}}{12} & \frac{\sqrt{6}}{12} + \frac{1}{2} & 0 \\\hline & \frac{4}{9} - \frac{\sqrt{6}}{36} & \frac{\sqrt{6}}{36} + \frac{4}{9} & \frac{1}{9} \\ \end{array}\]