Lecture 16: Derivation of Implicit Runge-Kutta methods
Using (6.6), the expansion for defined by (6.2) may be written as
where the coefficients are given by (6.7). Comparing this with the expansion (6.4) for , we see that the two stage implicit Runge-Kutta method will have order one if
defined by (6.2) may be written as 
are given by (6.7). Comparing this with the expansion (6.4) for 
, we see that the two stage implicit Runge-Kutta method will have order one if 
