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MathGroup Archive 2002

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Re: NDSolve with side conditions:

  • To: mathgroup at smc.vnet.net
  • Subject: [mg32751] Re: NDSolve with side conditions:
  • From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
  • Date: Fri, 8 Feb 2002 03:49:24 -0500 (EST)
  • Organization: Universitaet Leipzig
  • References: <a3tkmi$7e9$1@smc.vnet.net>
  • Reply-to: kuska at informatik.uni-leipzig.de
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,

Mathematicas build-in NDSolve command can't solve an algebraic
differential equation. Since numerical solvers for algebraic
differential
equations are an active area of research you should look
into the literature/netlib library to find a suitable algorithm.

Regards
  Jens

Thomas Steger wrote:
> 
> The following ordinary differential equation system is given:
> y'(t)=f1[y(t),x(t),z(t)]; x'(t)=f2[y(t),x(t),z(t)] and
> z(t)=f3[y(t),x(t)]. z(t) is given in implicite and integrated form.
> 
> The question reads as follows: Can Mathematica solve this system
> numerically by NDSolve. I have tried the following syntax:
> NDSolve[{y'[t]==f1[y[t], x[t], z[t]], x'[t]==f2[y[t], x[t], z[t]],
> z(t)==f3[y[t], x[t]], y[0]==y0, x[0]==x0, z[0]==z0},{y[t], x[t],
> z[t]},{t, 0, 100}].
> 
> I could differentiate z(t)=f3[y(t),x(t)] with respect to t; this would
> yield  a standard 3-dimensional DES. But I would like not to increase
> the dimension.
> 
> Thanks for any help!


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