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First of all, I don't really know what method I'm going to use to solve these differential equations. I know how to do Euler's method, and Runge-Kutta and those things, but perhaps there's a math library out there for C that works magic with differential equations. I don't really care how these equations get solved. I just care that they get solved, but I'm more than willing to write some code myself to solve them. If anybody has any suggestions, that'd be extremely appreciated.

Also, I don't really know how I'm going to solve 3 equations at once. If I write my own differential equation solver, I'm going to substitute and make them first order, then solve again, but I don't really know how to deal with equations that depend on eachother. :/

These are the equations:

[tex]\ddot{t} = \frac{-2M \dot{r} \dot{t}}{r(r-2M)}[/tex]

[tex]\ddot{\phi} = \frac{-2\dot{r}\dot{\phi}}{r}[/tex]

[tex]\ddot{r} = \frac{M\dot{r}^2}{r(r-2M)} - \frac{M(r-2M)}{r^3}\dot{t}^2 + (r - 2M) \dot{\phi}^2[/tex]

Dots mean differentiation with respect to [tex]\tau[/tex].

How do you solve 3 differential equations that all depend upon eachother at once (numerically)?

Any help would be greatly appreciated.