Finite difference method for electrostatic potential and field simulation

This paper presents a numerical solution to the two-dimensional Poisson equation using the finite difference method over a square domain. The partial differential equation is discretized using finite difference approximations subject to Dirichlet boundary conditions. The resulting system of linear equations is solved iteratively to solve potential distributions for various charge configurations. Potential distribution and electric field lines of point charge, dipole and quadrupole are simulated in the study. The numerical implementation is performed in Python, an open-source programming language.