# What is difference between numerical solution and approximation?

Lets say I have a problem, for example, initial or boundary value problem. I can't solve the problem analitically. From the literature it is known some appropriate techniques to solve the problem.

Question. What is difference in terminology between numerical and approximate techniques?

I have confused because numerical techniques include an approximation of the analitical solution.

• See Numerical analysis: "Numerical analysis is the study of algorithms that use numerical approximation (as opposed to general symbolic manipulations) for the problems of mathematical analysis". – Mauro ALLEGRANZA Dec 12 '17 at 9:08
• You can "approximate" also an "analitic" solution: we know that $\pi$ is blah, blah, but in order to compute it we have to stop at a certain point: the result of the computation nis obviously an approximation of $\pi$. – Mauro ALLEGRANZA Dec 12 '17 at 9:10