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.