# System of PDEs which is tricky for PDEPE

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I have a system of PDEs, mainly diffusion equations of the form:

T_t-(k(x)(T_x)_x=a*E^2

c_t-(D(x)*c_x)_x=d*(E_x+c_x-T_x)

(epsilon*E)_x=-b*c

Where a and d are constants and _t,_x represent partial differentiation w.r.t. t and x respectively. In terms of pdepe, I would have: f=0 for the third equation. Would this cause errors in the code?

I'm also struggling to see how I can input the boundary conditions.

Any suggestions?

##### 5 Comments

Bill Greene
on 24 May 2018

### Answers (5)

Torsten
on 23 May 2018

Edited: Torsten
on 23 May 2018

"pdepe" is designed to solve systems of parabolic-elliptic pdes. Your third pde is hyperbolic in nature. Thus "pdepe" is not suited to solve your system.

You will have to discretize your equations in space and solve the resulting system of ordinary differential equations using ODE15S.

Look up "method-of-lines" for more details.

Best wishes

Torsten.

##### 2 Comments

Torsten
on 23 May 2018

Torsten
on 24 May 2018

You could try to use "pdepe" with the third equation differentiated:

(epsilon*E)_xx=-b*c_x

with Dirichlet boundary condition

E = E0

at one end of the interval and

(epsilon*E)_x + b*c=0

at the opposite end.

Best wishes

Torsten.

Precise Simulation
on 9 Jun 2018

##### 0 Comments

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