Theory and Modern Applications
Table 1 Butcher array for FIRK and DIRK subclasses of the three-stage IRK methods (see [7])
(a) FIRK | (b) DIRK |
|---|---|
\(\begin{array} {c|cccc} c_{1} & a_{11} & a_{12} & a_{13}\\ c_{2} & a_{21} & a_{22} & a_{23}\\ c_{3} & a_{31} & a_{32} & a_{33}\\ \hline & b_{1} & b_{2} & b_{3} \end{array} \) | \(\begin{array} {c|cccc} c_{1} & a_{11} & 0 & 0\\ c_{2} & a_{21} & a_{22} & 0\\ c_{3} & a_{31} & a_{32} & a_{33}\\ \hline & b_{1} & b_{2} & b_{3} \end{array} \) |