# Thread: Non homogenous laplace PDE on a square

1. ## Non homogenous laplace PDE on a square

Hello,
I've tried to solve the attached PDE, as is shown in the file.
As is stated in the file, it seems unreasonable that U1 explodes so I hope you'll find the error in what I did.

2. Originally Posted by zokomoko
Hello,
I've tried to solve the attached PDE, as is shown in the file.
As is stated in the file, it seems unreasonable that U1 explodes so I hope you'll find the error in what I did.

Is u(x,y) to satisfy that equation inside or outside the square? Typically solutions to Laplace's equation, given the value on some closed curve, have very different solutions inside and outside the curve.

3. Originally Posted by zokomoko
Hello,
I've tried to solve the attached PDE, as is shown in the file.
As is stated in the file, it seems unreasonable that U1 explodes so I hope you'll find the error in what I did.

Typically Laplace equation is on some domain D (inside) so

$u_{xx} + u_{yy} = 0\; \text{ in}\; [0,1] \times [0,1]$ with your BC's on the boundary of this domain.

4. ## hey

I don't think I quite follow, I meant that U1 as a series doesn't converge (for almost all x,y).
The PDE as you said, is indeed defined inside [0,1]X[1,0].

I think there must be a mistake because the U1 is supposed to be a convergent series.

5. Originally Posted by zokomoko
I don't think I quite follow, I meant that U1 as a series doesn't converge (for almost all x,y).
The PDE as you said, is indeed defined inside [0,1]X[1,0].

I think there must be a mistake because the U1 is supposed to be a convergent series.
It'll converge. You must remember that $k_n$ involves $n$ and has the form

$k_n = \frac{a_n}{\sinh n \pi }$ where $a_n = 2 \int_0^1 f_1(x) \sin n \pi x\, dx$