# Question:How to solve system of PDE in composite domain? Help needed.

## Question:How to solve system of PDE in composite domain? Help needed.

Maple

I tried solving a system of PDEs in composite domain (see the attached image below), but couldn't get pdsolve to work for some reason. The error I got is: "Error, (in pdsolve/numeric) initial/boundary conditions must be defined at one or two points for each independent variable."

Would someone please let me know what I did wrong?

Here are the codes:

tmax := 1000:
Rsp := 8*10^(-6):
Rsn := 12.5*10^(-6):
ep := 0.385:
es := 0.724:
en := 0.485:
efp := 0.25e-1:
efn := 0.326e-1:
Lp := 183*10^(-6):
Ls := 52*10^(-6):
Ln := 100*10^(-6):
brugg := 1.5:

D0 := 7.5*10^(-10):
Dp := D0*ep^brugg:
Ds := D0*es^brugg:
Dn := D0*en^brugg:

c0 := 2000:

L := Lp + Ls + Ln:

Jp := 1:
Js := 0:
Jn := 2:

pdes :=  {

ep*(diff(cp(x, t),t)) - Dp*(diff(cp(x,t),x\$2)) - Jp = 0,
es*(diff(cs(x, t),t)) - Ds*(diff(cs(x,t),x\$2)) = 0,
en*(diff(cn(x, t),t)) - Dn*(diff(cn(x,t),x\$2)) - Jn = 0

};

conds := {cp(x, 0) = c0, cs(x, 0) = c0, cn(x, 0) = c0, #ICs
D[1](cp)(0, t) = 0, D[1](cn)(L, t) = 0, # BCs
cp(Lp, t) = cs(Lp, t), cs(Lp+Ls, t) = cn(Lp+Ls, t),
-Dp*D[1](cp)(Lp, t) = -Ds*D[1](cs)(Lp, t), -Ds*D[1](cp)(Lp+Ls, t) = -Dn*D[1](cn)(Lp+Ls, t)};

pdSol := pdsolve(pdes, conds, numeric, time = t, range = 0..L, spacestep = L/100, timestep = tmax/100);

﻿