Radau-I Runge-Kutta Methods

Radau IA

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

\[\begin{array}{r|rr} 0 & \frac{1}{4} & - \frac{1}{4} \\ \frac{2}{3} & \frac{1}{4} & \frac{5}{12} \\\hline & \frac{1}{4} & \frac{3}{4} \\ \end{array}\]

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

\[\begin{array}{r|rrr} 0 & \frac{1}{9} & - \frac{\sqrt{6}}{18} - \frac{1}{18} & - \frac{1}{18} + \frac{\sqrt{6}}{18} \\ \frac{3}{5} - \frac{\sqrt{6}}{10} & \frac{1}{9} & \frac{7 \sqrt{6}}{360} + \frac{11}{45} & \frac{11}{45} - \frac{43 \sqrt{6}}{360} \\ \frac{\sqrt{6}}{10} + \frac{3}{5} & \frac{1}{9} & \frac{11}{45} + \frac{43 \sqrt{6}}{360} & \frac{11}{45} - \frac{7 \sqrt{6}}{360} \\\hline & \frac{1}{9} & \frac{\sqrt{6}}{36} + \frac{4}{9} & \frac{4}{9} - \frac{\sqrt{6}}{36} \\ \end{array}\]

Radau IB

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

\[\begin{array}{r|rr} 0 & 0 & 0 \\ \frac{2}{3} & \frac{1}{3} & \frac{1}{3} \\\hline & \frac{1}{4} & \frac{3}{4} \\ \end{array}\]

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

\[\begin{array}{r|rrr} 0 & 0 & 0 & 0 \\ \frac{3}{5} - \frac{\sqrt{6}}{10} & \frac{\sqrt{6}}{75} + \frac{3}{25} & \frac{\sqrt{6}}{120} + \frac{1}{5} & \frac{7}{25} - \frac{73 \sqrt{6}}{600} \\ \frac{\sqrt{6}}{10} + \frac{3}{5} & \frac{3}{25} - \frac{\sqrt{6}}{75} & \frac{7}{25} + \frac{73 \sqrt{6}}{600} & \frac{1}{5} - \frac{\sqrt{6}}{120} \\\hline & \frac{1}{9} & \frac{\sqrt{6}}{36} + \frac{4}{9} & \frac{4}{9} - \frac{\sqrt{6}}{36} \\ \end{array}\]