Question

why we need approximation methods?

Answer 1

The argument goes (for approximation methods) that we don't have the mathematical tools or technologies necessary to solve some of the equations put forth by theories like Quantum, String and Chaos. In these instances, we do our best by approximating the equations so we get some rough idea of what it is they predict.

Answer 2

thank you

Answer 3

That is so not only for exotic topics like string theory where we do no know the tools. Even in most practical problems in engineering, even though we do know the equations, they cannot be solved exactly, and need numerical methods.