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MathGroup Archive 2006

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NDSolve system of partial eqn

  • To: mathgroup at smc.vnet.net
  • Subject: [mg66349] NDSolve system of partial eqn
  • From: Peter Breitfeld <phbrf at t-online.de>
  • Date: Wed, 10 May 2006 06:34:18 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

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 please explain it to me?
  
Gruss Peter
-- 
==-==-==-==-==-==-==-==-==-==-==-==-==-==-==-==-==-==-==-==-==-==
Peter Breitfeld, Bad Saulgau, Germany -- http://www.pBreitfeld.de


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