Why do we find the approximate solution?
 

I have a silly question-

Why do we find out the approximate solutions in various numerical methods , when we already have the exact solution, with which we compare it in order to estimate the error?

Another question is-

What are 'a priori' and 'a posteriori' error? whats the difference between them?

I hope someone helps.

Thanks in anticipation. Meena

Re: Why do we find the approximate solution?
 

I have a silly answer:

For how many *real* problems of interest do exact solutions actually exist?

Also, 'a priori' = before analysis is performed, 'a posteriori' = afterwards. Nearly every error estimate I've ever seen is a posteriori.