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.
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.
Thank you in advance
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.
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.
Thank you in advance
Typically Laplace equation is on some domain D (inside) so
$\displaystyle u_{xx} + u_{yy} = 0\; \text{ in}\; [0,1] \times [0,1]$ with your BC's on the boundary of this domain.
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.
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 $\displaystyle k_n$ involves $\displaystyle n$ and has the form
$\displaystyle k_n = \frac{a_n}{\sinh n \pi }$ where $\displaystyle a_n = 2 \int_0^1 f_1(x) \sin n \pi x\, dx$