Finite difference discretization for 2D Poisson's equation

[@palakkapoor5586]

Please explain it for robin boundary condition.

[@yasharvahedein4632]

Thank you for the very informative videos.

[@aminiahad5873]

Thanks a lot
Unfortunately.. I didn't learn ...how multiplied and divided blocks in the end of it

[@tag_of_frank]

If the boundary conditions are zero, wouldn't U(1 , : ) = U(99 , : ) = U( : , 1) = U( : , 99) = 0 ?
Instead, the value of U grows along these boundaries, and is only approximately zero at the corners, like U(1,1). Is this error ? Or is it because U(0, : ) is not in the reshaped matrix?
For example, I expected all zeros when I computed :
u( 1 , : ) =
Columns 1 through 12
0.0003 0.0005 0.0007 0.0009 0.0010 0.0012 0.0013 0.0014 0.0015 0.0017 0.0018 0.0019
Columns 13 through 24
0.0020 0.0020 0.0021 0.0022 0.0023 0.0024 0.0024 0.0025 0.0025 0.0026 0.0027 0.0027
Columns 25 through 36
0.0028 0.0028 0.0029 0.0029 0.0029 0.0030 0.0030 0.0030 0.0031 0.0031 0.0031 0.0032
Columns 37 through 48
0.0032 0.0032 0.0032 0.0032 0.0033 0.0033 0.0033 0.0033 0.0033 0.0033 0.0033 0.0033
Columns 49 through 60
0.0033 0.0033 0.0033 0.0033 0.0033 0.0033 0.0033 0.0033 0.0033 0.0033 0.0033 0.0032
Columns 61 through 72
0.0032 0.0032 0.0032 0.0032 0.0031 0.0031 0.0031 0.0030 0.0030 0.0030 0.0029 0.0029
Columns 73 through 84
0.0029 0.0028 0.0028 0.0027 0.0027 0.0026 0.0025 0.0025 0.0024 0.0024 0.0023 0.0022
Columns 85 through 96
0.0021 0.0020 0.0020 0.0019 0.0018 0.0017 0.0015 0.0014 0.0013 0.0012 0.0010 0.0009
Columns 97 through 99
0.0007 0.0005 0.0003

[@KM-bn9jf]

Hi Fahraynk.. I have this question too.. were you able to find out what needs to be modified in Matrix A to incorporate the boundary condition.

[@tag_of_frank]

At the time I had figured it out, I believe as long as it is zero on the edges, and if it varies from zero off of the edges it is maybe approximation error.
Not sure if that is exact answer, I figured this out months ago so barely remember now.
I found this video though, this guy explains poissons matrices very well : th-cam.com/video/-tlwQXewrYU/w-d-xo.html
Good luck man

[@KM-bn9jf]

Thank you for your reply. The video link was helpful.

[@trendytrenessh462]

Thank you very much