How can I use pdepe to solve a PDE with an integral boundary condition?

I would like to solve a PDE of the form

du(x,t)/dt = - du/dx - u

with the boundary condition

u(0,t) = int(u(x,t),x0,xf).

Since the usual @bcfun does not have argument u, is this boundary condition possible? If so, how would I formulate it?

Thanks in advance for any help.

Answer 1

[Youssef Khmou]

why not solve, first, for u(0,t) for known x0 and xf, using integral or quad or trapz next follow the routine ?

[Jessica]

Thanks for the suggestion, Youssef. If I were writing my own PDE solver, I'm sure that I would follow such a scheme. However, I would like to use the PDE solver that is built in to Matlab, pdepe.

Answer 2

[Youssef Khmou]

hi, take a look at the file,