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