5. Comparison with the exact solution.

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

we get

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.