I am a relatively new user of Maple, and I try to solve numerically the following PDE system :
> pde01 := diff(c(z, t), t) = (diff(c(z, t), z, z))-(diff(c(z, t), z))+k*(a-c(z, t));
> pde02 := diff(b(z, t), t) = (diff(b(z, t), z, z))-(diff(b(z, t), z))+k*(a-b(z, t));
> cl1 := c(0, t) = piecewise(t <= 0.3, 100, 0.3 < t and t <=0 .5, 200, 0.5 < t, 100);
> cl2 := c(l, t) = b(l, t);
> cl3 := (D(c))(l, t) = (D(b))(l, t);
> cl4 := b(L, t) = a;
> ci1 := c(z, 0) = 100; ci2 := b(z, 0) = 100;
> ibc := [cl1, cl2, cl3, cl4, ci1, ci2];
> pds01 := pdsolve([pde01, pde02], ibc, numeric, time = t, range = 1 .. 100);
The first equation is valid from z = 0 to z = l, and the second from l to infinity and the equations are coupled via the boundary conditions at the interface (z = l).
When I try to solve this, I keep receiving the following error message, whatever I do:
Error, (in pdsolve/numeric) initial/boundary conditions must be defined at one or two points for each independent variable.
The equations considered separately have an analytical solution, but the final aim is to solve a more complicated system, so it would be nice if I could already solve this one...
Thanks a lot,