Mathematica newbie question : NDSolve

• To: mathgroup at smc.vnet.net
• Subject: [mg40125] Mathematica newbie question : NDSolve
• From: sriramr at asdl.gatech.edu (Sriram Rallabhandi)
• Date: Fri, 21 Mar 2003 02:38:37 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```Hi,
I'm new to Mathematica. I'm using the following code to solve a
bi-harmomic PDE in two parameters u,v. The final output is the 3D
coordinate values: x[u,v],y[u,v],z[u,v]. I get the error attached even
though i have the boundary and initial conditions specified.
Can someone point me in the right direction??

a = 1;
rx1  = 0.7;
rx2  = 0.5;
ry1  = 0.6;
ry2  = 0.4;
z1  =  0.4;
z2  =  1.8;

NDSolve[{D[x[u, v], u, u, u, u] + a^4*D[x[u, v], v, v, v, v] +
2*\(a\^2\) D[x[u, v], u, u, v, v] == 0.0,
D[y[u, v], u, u, u, u] + a\^4*D[y[u, v], v, v, v, v] +
2*a\^2*D[y[u, v], u, u, v, v] == 0.0,
D[z[u, v], u, u, u, u] + a\^4*D[z[u, v], v, v, v, v] +
2*a\^2*D[z[u, v], u, u, v, v] == 0.0, x[0, v] == rx1*Cos[v],
y[0, v] == ry1*Sin[v], z[0, v] == z1, x[1, v] == rx2*Cos[v],
y[1, v] == ry2*Sin[v], z[1, v] == z2,
Derivative[1, 0])[x])[0, v] == 0.8*Cos[v],
Derivative[1, 0])[x])[1, v] == 0.5*Cos[v],
Derivative[1, 0])[y])[0, v] == 0.8*Sin[v],
Derivative[1, 0])[y])[1, v] == 0.4*Sin[v],
Derivative[1, 0])[z])[0, v] == 0.4,
Derivative[1, 0])[z])[1, v] == -0.4,
x[u, 0] == x[u,2*Pi], y[u, 0] = y[u,2*Pi],
z[u, 0] = z[u,2*Pi]}, {x, y, z}, {u, 0, 1}, {v, 0, 2*Pi}]

ParametricPlot3D[Evaluate[{x[u, v], y[u, v], z[u, v]}  /. %], {u, 0,
1}, {v, 0, 2*Pi},
PlotPoints  -> 100])

NDSolve::"deql":
"The first argument must have both an equation and an initial
condition."

Thanks
Sriram

```

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