Solving 2D Laplace Equation with Boundary Conditions

[dzi]

Hi,

My 2D L.e.:

Uxx + Uyy = 0

with boundary conditions:

U (x,0) =x
U (0,y) =0
U (1,y) =1
U (x,1) =x

Please, need help with analytical sollution!

i'm trying to do smth like it is described in attachment pic, but i it's not working..

Thanks!

 

[CompuChip]

Try separation of variables:
$$U(x, y) = \xi(x) \eta(y)$$
then find trial solutions for both, work out the product and impose the boundary conditions.

That is the (most common, probably not the only) way to do it. If you want us to help you locate your error or give you a complete answer, you'll have to show some work.

 

[dzi]

dear CompuChip..

i solved equation numerical with finite diferencial method..
and also needed analytical sollution for comparison..

finaly few minutes ago i found my error..
huhh..
it wasn't placed in calculation like i was thinkig,
but in my Matlab program which i used for drawing sollution of equation..

i appreciate on quick answer,
thanks..