What Are the Best Free Alternatives to MATLAB for Simulating Equations?

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¿Software to simulate graphs?

Is there an alternative to MATLAB for simulating equations,

I am looking for a way of getting some intuition for some Convection Diffusion Equation. I would like to play around with it, simulate it, change its IC/BCs, having some interactive graphs and stuff.
 
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There are many choices.

There is python and the matplotlib (2D mostly).
There is octave/gnuplot combination
There is freemat (intended to be a free a-la-matlab environment)
Possibly Scilab...have not used it, but have heard good things about it.
and a few other choices that are ready to download in my Ubuntu machine: Euler, Maxima, etc. (just go to software downloads and filter for Scientific or Educational software).

these are all free (as in gratis) choices...I presume that's what you were looking for.
 

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