Butcher Tableau

Resources: page=126

---

The Butcher tableau is a convenient way of summarizing the coefficient of RK methods in a clean and compact way. The Butcher tableau reads as:

Examples

Explicit Euler

Where

$$\begin{array}{rl}s& =1\\ a_{11}=0,b_1& =1c_1=0\end{array}$$

The “mid-point” RK2 method

Where

$$\begin{array}{rl}s& =2\\ a_{11}=0,a_{12}& =0c_1=0\\ a_{21}=\frac{1}{2},a_{22}& =0c_2=\frac{1}{2}\\ b_1=0,& b_2=1\end{array}$$