Fehlberg RK5(4)6

\begin{align} \begin{array}{c|cccccc} & & & & & & \\ \frac{1}{4} & \frac{1}{4} & & & & & \\ \frac{3}{8} & \frac{3}{32} & \frac{9}{32} & & & & \\ \frac{12}{13} & \frac{1932}{2197} & - \frac{7200}{2197} & \frac{7296}{2197} & & & \\ 1 & \frac{439}{216} & -8 & \frac{3680}{513} & - \frac{845}{4104} & & \\ \frac{1}{2} & - \frac{8}{27} & 2 & - \frac{3544}{2565} & \frac{1859}{4104} & - \frac{11}{40} & \\ \hline & \frac{16}{135} & & \frac{6656}{12825} & \frac{28561}{56430} & - \frac{9}{50} & \frac{2}{55}\\ & \frac{25}{216} & & \frac{1408}{2565} & \frac{2197}{4104} & - \frac{1}{5} & \end{array}\end{align}