Re: NDSolve system of partial eqn

• To: mathgroup at smc.vnet.net
• Subject: [mg66396] Re: NDSolve system of partial eqn
• From: "Jens-Peer Kuska" <kuska at informatik.uni-leipzig.de>
• Date: Thu, 11 May 2006 02:15:59 -0400 (EDT)
• Organization: Uni Leipzig
• References: <e3sh0g\$lu0\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Hi,
you have the solution for \[Phi][z,t]
but you ask NDSolve[] to find it and
NDSolve[] don't like this, eliminate \[Phi][z,t]
and it should work

Regards
Jens

"Peter Breitfeld" <phbrf at t-online.de> schrieb im
Newsbeitrag news:e3sh0g\$lu0\$1 at smc.vnet.net...
|
| I want to solve the following system of partial
deqns .
|
| \[Mu] = 0.01;
| \[Gamma] = 0.03;
| \[Rho] = 1000;
| Subscript[\[Delta], \[Epsilon]] = 0.171;
| K = 0.008;
| g = 9.81;
| Subscript[k, \[Alpha]] = 1.52;
|
| Subscript[L, 0] = 0.0003;
| Subscript[D, eff] = 3.7/10^9;
| Subscript[\[Epsilon], 0] = 0.1;
| H = 1;
| Subscript[t, max] = 1000;
|
| eqn1 = D[\[Epsilon][z, t], t] + D[\[Phi][z, t],
z] == 0;
| eqn2 = \[Phi][z, t] ==  (K*L[z,
t]^2*\[Epsilon][z, t]^(3/2)*(\[Rho]*g +
|       Subscript[\[Delta],
\[Epsilon]]^(1/2)*\[Gamma]* D[1/(L[z, t]*
|          \[Epsilon][z, t]^(1/2)),
|         z]))/\[Mu];
|
| eqn4 = D[L[z, t], t] == Subscript[D, eff]* ((1 -
Subscript[k, \[Alpha]]*
|         \[Epsilon][z, t]^(1/2))^2/ L[z, t]);
|
| NDSolve[{eqn1, eqn2, eqn4,
|   \[Epsilon][z, 0] == Subscript[\[Epsilon], 0],
|   L[z, 0] == Subscript[L, 0],
|   \[Phi][-H, t] == 0,
|   \[Phi][0, t] == 0},
|  {\[Epsilon], \[Phi], L}, {z, -H, 0},
|  {t, 0, 1}]
|
| Trying to solve this, I get the Error
"NDSolv::ivone", but I don't
| really understand what I did wrong. Can someone
|
| Gruss Peter
| --
|
==-==-==-==-==-==-==-==-==-==-==-==-==-==-==-==-==-==-==-==-==-==
| Peter Breitfeld, Bad Saulgau, Germany --
http://www.pBreitfeld.de
|

```

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