       Re: Simplifying a second order eq. system

• To: mathgroup at smc.vnet.net
• Subject: [mg46039] Re: Simplifying a second order eq. system
• From: Paul Abbott <paul at physics.uwa.edu.au>
• Date: Tue, 3 Feb 2004 03:21:29 -0500 (EST)
• Organization: The University of Western Australia
• References: <bvd7jv\$51v\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```In article <bvd7jv\$51v\$1 at smc.vnet.net>,
"Gunnar Lindenblatt" <Gunnar.Lindenblatt at pobox.com> wrote:

> For example, to get the telegraph equation by self-induction and capacitive
> coupling:
>
> (One can solve this problem on the space of a postage stamp...)

I doubt that you can solve the problem on a postage stamp. You can,
however, eliminate i (or u) to uncouple the differential equations.

> In := Remove["Global`*"]
>
> In := myEqn1 = -Dt[u,x] == r i + l Dt[i,t]
>
> In := myEqn2 = -Dt[i,x] == s u + c Dt[u,t]
>
> ....
>
> Third try: Using "Eliminate"
>
> In := Eliminate[{myEqn1,myEqn2}, {Dt[i,x],Dt[i,t]}]
>
> results:
>
> True
>
> That's fine! However, it does not really help me...

Correct -- but you're on the right track here.

> (By the way, the result should be:
>
> Dt[u,{x,2}]== r s u + (r c + l s) Dt[u,t] + l c Dt[u,{t,2}])

So you want to eliminate i. You need to consider the original equations
and their derivatives then:

SetAttributes[{r, l, s, c}, Constant]

Simplify[Eliminate[{myEqn1, myEqn2, Dt[myEqn1, x], Dt[myEqn2, t]},
{Dt[i, t, x], Dt[i, x], Dt[u, x]}]]

Cheers,
Paul

--
Paul Abbott                                   Phone: +61 8 9380 2734
School of Physics, M013                         Fax: +61 8 9380 1014
The University of Western Australia      (CRICOS Provider No 00126G)
35 Stirling Highway
Crawley WA 6009                      mailto:paul at physics.uwa.edu.au
AUSTRALIA                            http://physics.uwa.edu.au/~paul

```

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