Laplace Equation Numerical Solution

[jawad hussain]

Homework Statement

Place a charge of +1 mC at the centre of the square, and initially
using the relaxation method, solve the potentials inside the grid for
the boundary conditions:
• N=S=E=W=10 V
• N=S=10 V; E=W=−10 V
• N=0 V; E=10 V; S=20 V; W=30 V

Relevant Equations

Laplace Equation, Poisson equation

I wonder how to incorporate point charge?

 

[haruspex]

Perhaps an application of conformal mapping, with an inversion at the point?
Or maybe make it a square too, then take the limit as it shrinks to a point.