# Numerical Methods - which one for which problem?

## Main Question or Discussion Point

Can anyone tell me for which problems you should use these numerical methods:

- finite difference method
- finite element method
- boundary element method
- method of moments

For example I read that finite element method is often used for car crash simulations, and that it gives very good results, but what about other methods, when you would use them? Any real-life example?

SteamKing
Staff Emeritus
Homework Helper
Why don't you google them and find out for yourself?

I really tried to find it on Google, you see that: "I read that finite element method is often used for car crash simulations", I found that using Google, but for other methods I hadn't have success.

HallsofIvy
Homework Helper
Frankly your question doesn't make a whole lot of sense! Part of the "art" of "Applied Mathematics" is being able to decide which method is best for a specific application. There is NO general rule of "use this method for that problem".

Thanks to both of you. ;)

Lets say that I found what I was looking for, when we're talking about EM problems.

"2.An EM problem in the form of a partial differential equation can be solved using the
finite difference method. The finite difference equation that approximates the differential
equation is applied at grid points spaced in an ordered manner over the whole solution
region. The field quantity at the free points is determined using a suitable method.
3. An EM problem in the form of an integral equation is conveniently solved using the
moment method. The unknown quantity under the integral sign is determined by matching
both sides of the integral equation at a finite number of points in the domain of the
quantity.
4. While the finite difference method is restricted to problems with regularly shaped solution
regions, the finite element method can handle problems with complex geometries.
This method involves dividing the solution region into finite elements, deriving equations
for a typical element, assembling all elements in the region, and solving the resulting
system of equations."

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