DC conduction equation in Matlab

[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

 

[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.

 

[Mattw]

Hi jfgobin

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

 

[jfgobin]

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

What is your second equation?

 

[jfgobin]

Or is is just Maxwell's?

 

[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 can't 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