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Flat Earth Investigations / Re: Problems with the Heliocentric Model
« on: August 10, 2019, 04:03:51 PM »Please explain the difference between an analytic solution and a numerical solution and how they are differentiated when it comes to a problem involving math?This post sums it up nicely:
https://www.quora.com/What-is-the-difference-between-a-numerical-and-an-analytical-solution
An analytical solution is exact.
A numerical solution is an approximation that's used when an analytical solution is unavailable or unusable.
Maybe you remember using the trapesium rule to estimate the area under a curve in maths class - that's using a numerical method instead of an analytic one. If the curve was simple enough you could have just used calculus to integrate it get an exact solution and you wouldn't need to bother with the trapesium rule.
If you're doing this for a living you'd use more complicated algorithms than the trapesium rule, and you'd generally know how accurate your numerical solution is.
This is why we can say that not having an analytical solution to the three-body problem is okay. You compute a numerical solution and know how good your solution is. This means that if I want to know the position of Jupiter in X years with an accuracy of Y meters, I can do that.