## Solution to Laplace equation with simple boundary conditions

Hi, I've been learning how to use the 2D Laplace equation recently. I have problem concerning electric fields and I found this explanation - http://www.ph.utexas.edu/~mwguthrie/p.laplace.pdf where the boundary conditions are the same as mine -

V = 1 for x = 0
V = 0 for y = 0
V = 0 for y = 100
V = 0 for x = 100 (it says 10 on the guide but i assume this is just a typo as it says 100 everywhere else!)

and it then gives the equation for the solution. $v(x,y)=\dfrac{2}{\pi} \arctan\left( \dfrac{\sin(\frac{\pi y}{100})}{\sinh(\frac{\pi x}{100})}\right)$Which is mostly good - all the boundary conditions seem to be met APART from where x=100. it's worst for when y is around 50, i.e. for when x=100 and y=50, the value of v is 0.055 - not 0! Why does this happen? How can i modify the solution so this boundary condition is met?

thankyou!