# DC conduction equation in Matlab

1. Feb 14, 2013

### Mattw

Hello

I am solving DC conduction equation in Matlab. My equation is 1/r * ∂/∂r [r*σ* ∂V/∂r]=∂ρ/∂t
My equation is 1D(only varies with radius) and time dependent. i am using pdepe solver.The space charge ( ρ) is the time dependent variable. But the form of matlab pdepe solver the time dependent is the unknown term V. Can alyone help me how to solve this equation with pdepe or other solvers.

Thanks

2. Feb 14, 2013

### jfgobin

Good Morning Mattw,

So, a few questions:

Your unknown is $V\left(t,r\right )$?
$\rho \left (t,r\right)$ is known for all $t$ and $r$?

J.

3. Feb 14, 2013

### Mattw

Hi jfgobin

the space charge distribution ρ(t,r) is unknown.

4. Feb 14, 2013

### jfgobin

Mattw, so you are trying to solve for both $V$ and $\rho$.

5. Feb 14, 2013

### jfgobin

Or is is just Maxwell's?

6. Feb 14, 2013

### Mattw

Hi jfgobin

ρ(t,r) is just the continuti equation from Maxwell's.

I am solving this equation with matlab, and i am using pdepe solver. at the beginning if i assume my problem is in steady state then i can make ∂ρ/∂t zero. But the problem is i cant make "C"( coefficient of the time dependent term) zero in pdepe solve. Do you have any idea if there is matlab PDE solver for 1/r * ∂/∂r [r*σ* ∂V/∂r]=0 OR how to make "c" zero in pdepe solver?

Thanks