Why am I getting this error?

• To: mathgroup at smc.vnet.net
• Subject: [mg60341] Why am I getting this error?
• From: ksmath <kdsimon at uiuc.edu>
• Date: Tue, 13 Sep 2005 06:07:51 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```I am attempting to solve a system with 3 pde's and I keep getting this error even though I think all of my equations have independent variables:

NDSolve::dvnoarg: The function v appears with no arguments.

If anyone could find the mistake in my code I would really appreciate it.  C,V, and R are the dependent variables, and t (time) and x(distance-does not depend on time) are the independent variables.  All other variables are constants.

Thank you for any assistance you can provide me.

\!\(\(rRHS\  = \ \(d\_r\) D[r[t,
x], {x, 2}] + Î² \((1 - \((r[t, x] - r\_base)\)/\((k\_r -
r\_base)\))\) \((r[t, x] - r\_base)\);\)\[IndentingNewLine]
\(vRHS\  = \ \(d\_v\) D[v[t, x], {x, 2}] - Ï?\ v[t, x]\  -
Î·\ v[t, x]\ c[t, x]/\((Î³\_1 + v[t, x])\) + If[
q\_large < q\_min, Î» \((q\_large - q\_min)\), 0];\)\[IndentingNewLine]
\(\(cRHS\  = \ D[c[t, x]\ v[t, x]\ D[v[t, x], x], x] + If[v[
t, x] â?¥ v\_g, Ï?\ v[t, x]\ c[t,
x]\ /\((Î³\_2 +
v[t, x])\), Ï? \((v[t, x] -
v\_d)\) c[t, x]];\)\(\[IndentingNewLine]\)
\)\[IndentingNewLine]
\(reqn\  = D[r[t, x], t]\  == \ rRHS;\)\[IndentingNewLine]
\(veqn\  = \ D[v[t, x], t]\  == \ vRHS;\)\[IndentingNewLine]
\(ceqn\  = \ D[c[t, x], t]\  == \ cRHS;\)\)

BC1 = Derivative[0, 1][r][t, 0] == 0;
BC2 = Derivative[0, 1][r][t, 1] == 0;
BC3 = Derivative[0, 1][v][t, 0] == 0;
BC4 = Derivative[0, 1][v][t, 1] == 0;
BC5 = c[t, 0] == 1;
BC6 = c[t, 1] v[t, 1] Derivative[0, 1][v][t, 1] == 0;

\!\(\(c\_init = \(c\_o\) Exp \((\(-150\) x\^2)\) == c[0,
x];\)\[IndentingNewLine]
\(r\_init = \((K\_r -
r\_base)\) Exp \((\(-100\) x\^2)\) + r\_base == r[0, x];\)\
\[IndentingNewLine]
\(v\_init = \((v\_g - v\_d)\)/\((2  v\_o)\) == v[0, x];\)\)

\!\(\(solution\  = \ NDSolve[{reqn, \ veqn, \ ceqn, q1\_i,
q2\_i, \ c\_init, \ v\_init, \
r\_init, \ BC1, \ BC2, \ BC3, \ BC4, \ BC5, \ BC6}, {r[t, x], v[t,
x], c[t, x], q1[t, x], q2[t, x]}, {t, 0, 1}, {x, 0, 1}];\)\)

Any help is much appreciated.

Katie

```

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