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MathGroup Archive 2004

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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[1] := Remove["Global`*"]
> 
> In[2] := myEqn1 = -Dt[u,x] == r i + l Dt[i,t]
> 
> In[3] := myEqn2 = -Dt[i,x] == s u + c Dt[u,t]
> 
> ....
> 
> Third try: Using "Eliminate"
> 
> In[6] := 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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