Laplace Equation using FDM

[idowuh]

Uxx + Uyy = 0U(x,y ) = Log [(x+1)2 + y2]0 ≤ x; y ≤ 1please i need help on this exercise. Anyone who can help will be appreciate.

 

[stapel]

Uxx + Uyy = 0U(x,y ) = Log [(x+1)2 + y2]0 ≤ x; y ≤ 1please i need help on this exercise. Anyone who can help will be appreciate.

Is everything meant to be one line with no super- or subscripts, or is the exercise more along the following lines?

. . . . .U_xx + U_yy = 0

. . . . .U(x, y) = Log[(x + 1)² + y²]

. . . . .x > 0

. . . . .y < 1

Either way, what are your thoughts? What have you tried? How far have you gotten? Where are you stuck?

Please be complete. Thank you!

 

[Ishuda]

Uxx + Uyy = 0U(x,y ) = Log [(x+1)2 + y2]0 ≤ x; y ≤ 1please i need help on this exercise. Anyone who can help will be appreciate.

Something is strange. A Finite Difference Method for the Laplace Equation generally requires a shape description and a (set of) either the value of U or its normal derivative on the boundary or a mixture of both (value along some portion(s) of the boundary and normal derivative along the other portions). So, is that U(x,y ) = Log [(x+1)2 + y2]0 ≤ x; y ≤ 1 supposed to be the boundary condition? That is, do we have a Dirichlet boundary condition problem where the boundary is semi-infinite:
U_xx + U_yy = 0,
U(x,y) = Log [(x+1)² + y²] on the boundary of D,
D={\(\displaystyle (x,y);\, 0\, \le x \lt\, \infty ,\ -\infty \lt\, y \le\, 1\)}?