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MathGroup Archive 2006

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Re: NDSolve with implicit function

  • To: mathgroup at smc.vnet.net
  • Subject: [mg65890] Re: NDSolve with implicit function
  • From: "Jens-Peer Kuska" <kuska at informatik.uni-leipzig.de>
  • Date: Fri, 21 Apr 2006 01:33:26 -0400 (EDT)
  • Organization: Uni Leipzig
  • References: <e27k92$5ft$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,

calcY[x_?NumericQ] :=
y /. FindRoot[Sin[x^2] + y - 1, {y, 1}][[1]]

sol = NDSolve[{x'[t] == Cos[x[t]*calcY[x[t]]], 
x[0] == 0}, x[t], {t, 0, Pi}];

Plot[Evaluate[x[t] /. sol[[1]]], {t, 0, Pi}];

Regards
  Jens

<rondeau at uvic.ca> schrieb im Newsbeitrag 
news:e27k92$5ft$1 at smc.vnet.net...
|I am trying to numerically solve a differential 
equation
| {x'[t]==f[x[t],y[t]], x[0]=a} , where y[t] is 
the numerical solution to an
| implicit function g[x[t],y[t]]==0 (not a 
polynomial).
|
| In other words, given x[t], we should be able to 
numerically compute y[t]
| from the implicit function and it would enter 
numerically into the function
| f of NDSolve.
|
| Anyone with an idea on how to do this?
|
| Thanks.
| Daniel
| 



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