Bogacki-Shampine RK5(4)8

\begin{align} \begin{array}{c|cccccccc} & & & & & & & & \\ \frac{1}{6} & \frac{1}{6} & & & & & & & \\ \frac{2}{9} & \frac{2}{27} & \frac{4}{27} & & & & & & \\ \frac{3}{7} & \frac{183}{1372} & - \frac{162}{343} & \frac{1053}{1372} & & & & & \\ \frac{2}{3} & \frac{68}{297} & - \frac{4}{11} & \frac{42}{143} & \frac{1960}{3861} & & & & \\ \frac{3}{4} & \frac{597}{22528} & \frac{81}{352} & \frac{63099}{585728} & \frac{58653}{366080} & \frac{4617}{20480} & & & \\ 1 & \frac{174197}{959244} & - \frac{30942}{79937} & \frac{8152137}{19744439} & \frac{666106}{1039181} & - \frac{29421}{29068} & \frac{482048}{414219} & & \\ 1 & \frac{587}{8064} & & \frac{4440339}{15491840} & \frac{24353}{124800} & \frac{387}{44800} & \frac{2152}{5985} & \frac{7267}{94080} & \\ \hline & \frac{587}{8064} & & \frac{4440339}{15491840} & \frac{24353}{124800} & \frac{387}{44800} & \frac{2152}{5985} & \frac{7267}{94080} & \\ & \frac{2479}{34992} & & \frac{123}{416} & \frac{612941}{3411720} & \frac{43}{1440} & \frac{2272}{6561} & \frac{79937}{1113912} & \frac{3293}{556956} \end{array}\end{align}