Simplify and then discretize a set of equations with derivatives and integrals

• To: mathgroup at smc.vnet.net
• Subject: [mg126650] Simplify and then discretize a set of equations with derivatives and integrals
• From: Matthieu Brucher <matthieu.brucher at gmail.com>
• Date: Tue, 29 May 2012 05:44:45 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com

```Hi,

I'm new to Mathematica, but as I professionally have access to it, I'd
like to use it to simplify this problem.

I have a set of equations (from http://www.simulanalog.org/statevariable.pdf)
explaining how a simple electronic system works. My input is e(t) and
my output is vd(t). f(v) can be written as an exponential function
(f(v) = a * e^(b * v + c) for instance).
Here are the equastions :

eqns = {e[t] - i[t] * R - vc[t] - vd[t] == 0,
vc[t] == 1/C * Integrate[i[t], t],
i[t] == f[vd[t]]}

What I'd like is first to simplify this set of equations to a simple
one with only e(t) and vd(t). At one point, I could get the correct
result, but I could get the correct result after resetting the kernel.

Once this is done, I'd like to discretize the resulting function with
the bilinear transform.

Of course, it easy to get the result by hand in this case. But my next
set of equations is so complicated that I don't want to try to solve
it (my main issue is the first step, the discretization is 'just"
symbolic computation once the replacement is done), so I'm back at
Mathematica.

Is it possible do this in Mathematica? Is it complicated to do?

Matthieu

```

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