Could someone please point me in the right direction for finding an analytical solution to the following (if one exists):
f is probably going to be a constant function and I will probably have constant initial and boundary conditions but they're not finalised yet, I'm just looking for a gentle nudge in the right direction or for someone to tell me that it's unsolvable so that I can use a numerical method.
Thanks in advance!
Ok I think I might be needing more than a gentle nudge as I don't really follow you and have never heard of a double Fourier series. I'm fairly sure all the boundary conditions will be the same constant value (lets say c1) and the initial condition will be another constant (c2). Could you guide me through it if it's not too much trouble?
I'll provide some guidence. First let so that the boundary conditions (I'm assuming that the square region is )
becomes
and the PDE becomes
We'll first consider the PDE without a source term ( ) then address it later.
Now assume separable solutions
so your PDE becomes
which gives
, where and are constants
with the boundary condition . Now we are a point like solving the heat equation in one space dimension.
Your turn - You pick it up from here.