boundary problem with NDSolve

• To: mathgroup at smc.vnet.net
• Subject: [mg33094] boundary problem with NDSolve
• From: "Borut L" <gollum at email.si>
• Date: Fri, 1 Mar 2002 06:52:41 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```Hi,

My problem is modeled with a system of four 1st order ODEs with four
boundary
conditions known. But when I enter these conditions, an error is produced:

NDSolve::"ndv": "For a boundary value problem, only nth order single linear
ordinary differential equations is supported."

I am solving for {x,y,a,F} and I specify numerical conditions for x[0],
y[0], x[1] and y[1].

NDSolve looks like this

In[31]:=
NDSolve[
{
x'[s] == Cos[a[s]],
y'[s] == Sin[a[s]],
F'[s] == Sin[a[s]] - b x[s] Cos[a[s]],
a'[s] == (Cos[a[s]] + b x[s] Sin[a[s]])/F[s],
x[0] == 0,
y[0] == 0,
x[1] == 0,
y[1] == -1
}
, {x, y, F, a}
, {s, 0, 1}
] // First

I don't understand the error message produced. Mathematica says it can't do
what I've given her (is it ok if I personify?).

Is it Cos[a[s]] and alike terms that ain't acceptable? They are not really
linear. If that's the catch, how to extend NDSolve to solve the system
above?

Otherwise, if I want to stay with Mathematica, I am forced to search for
solutions manually (by shooting) for various F[0] and a[0]. That could be
tedious. I think Numerical Recipies have this implemented, but I would be
happy to hear if something alike was already done for Mathematica. Was it?

Borut Levart

```

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