[thoth]

>A branch of physics used to be taught a long time ago called "numerical analysis" to deal with this issue.

Freshmen engineers had to take a year-long Numerical Analysis and FORTRAN programming class at my undergrad university. We would learn various iteration methods for solving equations and the homeworks would be more problems to solve with a program or two to write too.

This stuff is still taught, it just might be out of a different department than physics.