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How can I implicitly solve a single equation in Matlab?

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+2 A:

I would try using fzero, or if that encounters problems because of complex values/infinities, fminbnd.

Matt Mizumi 2010-08-24 14:54:21

Not to be confused with F-Zero. :) http://en.wikipedia.org/wiki/F-Zero_(video_game)

Doresoom 2010-08-24 15:01:21

Thanks for posting this, however, this function only gives the roots of the equation and not a numerical solution for M.Awesome game by the way :). Played the SNES version a LOT!

Ingo 2010-08-24 15:09:53

@Ingo: Both fzero and fminbnd are numerical solvers. I'm not sure if I understand your objection -- you can trivially rewrite the equation to have a zero on the right side, yes?

Matt Mizumi 2010-08-24 16:26:11

Matt is right -- all you have to do is `f = @(M) (Atemp/At)^2 -1/M^2*((2/(gamma+1))*(1+(gamma-1)*M^2/2))^((gamma+1)/(gamma-1)))` and `fzero(f,M0)` where `M0` is an initial guess, or `fminbnd` if required. If you need a symbolic solution, you'll need the MATLAB symbolic toolbox, in which case, it's a simple matter of just using the `solve()` command.

Gilead 2010-08-24 16:41:54

In fact, if `Atemp`, `At` and `gamma` are constants (which they are if you're solving for `M`), you can do a little bit of algebra to reduce your equation to `log(M) = C1 + C2*log(2 + C3*M^2)`, where C1, C2, and C3 are constants. Then you can use `fminbnd` and restrict `M` to be greater than some nonzero number, say 1e-6, to avoid 0 in the log term.

Gilead 2010-08-24 17:07:29

Thank you so much. I feel totally stupid right now. Figured the same out yesterday night with too much coffee after a too long time and forgot to post that before going to bed. You're right, so thanks again!

Ingo 2010-08-25 17:36:29

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How can I implicitly solve a single equation in Matlab?

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