The numerical solution satisfies
By the mean value theorem,
for
Subtracting this from (5.6) and setting
, we get
Now, if we assume that satisfies a Lipschitz condition in and , as will happen in practice, we get the following bounds:
and
(by using Lipschitz condition and mean value theorem)
for 
, we get 
satisfies a Lipschitz condition in 
and 
, as will happen in practice, we get the following bounds: 
