, and use it to
estimate to 2nd order, the value of 
given 
, 
and
.
Call the value we obtain in this way 
to indicate that it is the result of the
predictor step. In Taylor's theorem let Y be the state vector , and use it to
estimate to 2nd order, the value of given , and
.
Call the value we obtain in this way to indicate that it is the result of the
predictor step.
Where for some 
in 
...
As the differential equations only give us the value of the first derivative in terms
of time and value of the state variable, we need an estimate of the second derivative. Now
use Taylor's theorem again to estimate the value of using and
.
Note that this time we use 
in Taylor's theorem.
Where for some 
in 
...
Which we can solve for 
...
Now define 
.
Inserting this into the predictor...
Predictor
Where...
Which is...
