Re: ODE system - shooting for a terminal point

• To: mathgroup at smc.vnet.net
• Subject: [mg121178] Re: ODE system - shooting for a terminal point
• From: Oliver Ruebenkoenig <ruebenko at wolfram.com>
• Date: Sat, 3 Sep 2011 08:03:26 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <201108311004.GAA12094@smc.vnet.net>

```On Wed, 31 Aug 2011, The Mighty Algernon wrote:

> Hi,
>
> I wonder if you could help me.
>
> I have a system of ODE in which I have to figure out the initial
> conditions of part of the differential equations. I managed to do this
> by the shooting method by writing the system as a function of the
> initial conditions.
>
> For example solution[yini_,zini_]:=NDSolve[......
>
> then I used FindRoot on the set of terminal restrictions to find yini
> and zini (these are the initial conditions). This procedure worked
> although it is terribly sensitive to the first guesses on the FindRoot
> and some results I get are obviously wrong. But this is something I
> can refine.
>
> Now I have a similar goal but the variable I'm trying to guess is not
> an initial condition of a differential equation but the terminal value
> of the range of the exogenous variable. For example,
>
> If I have a system of 2 ODE , y[x] and z[x], I want to know for {x,
> 0,xtarget} what is my xtarget. Think of x as time and I want to figure
> when is the terminal time of the system such that some restrictions at
> the terminal time are met.

Hi,

perhaps this could be done as an Event?

Oliver

>
> My first ideia was to adapt the above procedure, writing
>
> solution[xtarget_]:=NDSolve[......
> then giving the set of restrictions and then using FindRoot to get
> xtarget, but Mathematica gives me an error message the xtarget is not
> a real value.
>
>
> My question is :
>
> Is it possible to adapt the procedure outlined above, meaning that
> I'm just doing some kind of error here (that I'll have to correct), or
> Mathematica does not handle this kind of problems directly in NDSolve
> and I have to write some sort of loop with ever more refined guesses
> for xtarget?
>
> My best regards
>
> Joao Pereira
>
>
>
>
>
>
>
>

```

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