Again consider the differential equation
As we said before, the exact solution is then
By using maclaurin expansion we know that
for small values of k. If we insert
Now compare with the approximate solution from last part
We see that the error E in the approximation thus is
for some dunctions m1(x), m2(x),… (that we can compute!). We say that the error E is of order and write E=O( ), where O stands for big ordo.