1. Find a Butcher Tableau

Hi there

Find the Butcher Tableau of the forth order method :

$\displaystyle k_1 = f(t_i , y_i)$

$\displaystyle k_2 = f(t_i + 0.5 h , y_i + \frac{h}{4}(k_1+k_2))$

$\displaystyle k_3 = f(t_i + h , y_i + hk_2)$

$\displaystyle y_{i+1} = y_i + \frac{h}{6} (k_1 + 4k_2 + k_3)$

Any help would be much appreciated

Best regards,
Rapha

2. butcher table

0 | 0 0 0
1/2 | 1/4 1/4 0
1 | 0 1 0
----------------
1/6 2/3 1/6

butcher tableau

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