Using pdepe to solve coupled PDEs with boundary condition with flux listed at two locations (implicit boundary condition)

Hi, I hoping someone can tell me if this is possible. I'm trying to solve 3 PDEs and one of them has the following boundary condition

(∂n_e (x=0,t))/∂x)=constans1*exp(fn of (∂n_e (x=0,t))/∂x))-constant2*exp(fn of (∂n_e (x=0,t))/∂x))

for brevity, I left out the constants in constants1 and constants2 and only listed that the exponential is a function of dn/dx.

Is it possible to specify this in matlab. To solve this problem, I'm currently define a variable in my pdefun function which gets the value of the derivate close to zero. Then this variables is passed into the BC as the right hand side of the boundary condition. However, this makes the code very slow and comparing to the Steady state solution, there is like 10% error.

Answer 1

[Torsten]

Hi Yuri,

I suggest you solve the equation

(∂n_e (x=0,t))/∂x)- Constants*exp(function of ∂n_e (x=0,t))/∂x))=0 (1)

in bcfun for ∂n_e (x=0,t))/∂x (using fzero, e.g.).

Then your boundary condition becomes

∂n_e (x=0,t))/∂x = solution of equation (1)

which fits the type of boundary condition that can be implemented in pdepe.

Best wishes

Torsten.