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Student Support Forum: 'NDSolve PDE Boundary conditions' topicStudent Support Forum > General > "NDSolve PDE Boundary conditions"

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afm
10/20/12 11:50am

Hello everybody,

I'm trying to solve a quite complex PDE (or even PDE system). I have a charge distribution which is one dependent variable. Now I want to compute the potential in dependence of time.
There are two ways to do it:
1. One uses the poisson-equation or
2. One integrates over the hole charge
However, no matter which version I use, I always get the error:
NDSolve::ivone: Boundary values may only be specified for one independent variable. Initial values may only be specified at one value of the other independent variable

If it helps, here is the system:

D[nn[r, z, t], t] ==
alpha[Norm[ve[r, z, t]]]*Norm[vd[r, z, t]]*nn[r, z, t]+
vd[r, z, t].Grad[nn[r, z, t]],
D[np[r, z, t], t] ==
alpha[Norm[ve[r, z, t]]]*Norm[vd[r, z, t]]*nn[r, z, t],

V[r, z, t] ==
1/4/Pi/e0*
HoldForm[Integrate[
Integrate[
Integrate[(np[r, z, t] - nn[r, z, t])/
Sqrt[(r - r1*Cos[ph])^2 + (r - r1*Sin[ph])^2 + (z -
z1)^2], {ph, 0, 2 Pi}], {r1, 0, 0.1}], {z1, 0, 0.3}]],
D[Q[r, z, t], t] ==
10^0,

nn[0.1, z, t] == 1,
nn[r, 0, t] == 1,
nn[r, z, 0] == 1,
Q[r, z, 0] == 10^-6,
np[r, z, 0] == 1

Thanks in advance...

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