If the method is of order , then we have

(8.6)

Therefore, form (8.5) and (8.6),

(8.7)

Now writing and noting that , we have then

(8.8)

Consequently, Equation (8.8) is a necessary and sufficient condition for a method to have order

If the polynomial is given, Equation (8.8) shows how a unique polynomial of degree can be found such that the method has order . This is illustrated by the following example.