2d Laplace equation in a 1/4 plane

[RedBranchKnight]

I wish to approximate the Laplace PDE in a 1/4 plane by truncation of the domain in (x,y) variables:

U_xx + U_yy = 0

Now the PDE is approximated in a box [0, xMax] X [0, yMax] and I can solve it using finite differences.

But the problems are:

1. How to choose xMAx, yMax appropriately
2. What boundary conditions (if any) at xMax, yMax

thanks

 

[RedBranchKnight]

Another option I am using is to transform the 1/4 plane domain in which Laplace PDE is defined into a unit square, for example using the transformation:

z1 = tanh(x)
z2 = tanh(y)

We then get a convection-diffusion PDE in z1 and z2.

Does anyone know of any sources to this approach?

thanks