A Butcher tableau is a compact display of the coefficients of a Runge-Kutta method:
 |  |
 |
For an 
-stage
method applied to 
,
the stages 
for 
and the update are
 |  |  |
(1)
|
 |  |  |
(2)
|
The method is explicit when 
for 
, in which case 
is strictly lower triangular.
