## Saturday, July 14, 2012

### Maxima/wxMaxima - solving for the roots of a transcendental equation

Ok, so something is wrong with my Python.  I think Spyder is giving me some fits in Ubunt for somereason.  Anyways, luckily I have Maxima and Sage to fall back on.  In order to solve for the roots of a transcendental equation, I provide a following example.

The equation I want to solve is:

$\tan \left( \tfrac{1}{2} C d^2 \right) - \tan \left( \tfrac{1}{2} C a^2 \right) = 0$

where $$\deta$$ is given.  I first plotted it to make sure it did in fact show trends of a root or roots for $$\delta = 0.5$$.

delta:0.5;
eqn(x):= tan(0.5*x*(delta^2)) - tan(0.5*x);
plot2d(eqn, [x, 0, 20],[y, -1, 1]);


So, yup, it definitely has roots.  The first root is actually at zero, but this is trivial in my case.  So I am interesting in the second root.  It seems to be around 8.  I choose the interval for the root finder to look on as 7.8 to 8.5.

find_root(tan(0.5*x*(delta^2)) - tan(0.5*x), x, 7.8, 8.5);
8.377580409572781


So the root found is the bold number above!