Poisson’s equation

Poisson's equation is a second-order partial differential equation that is a special case of Laplace's equation. While Laplace's equation has solutions that equal zero, Poisson's equation is represented as (\nabla^2 V = f), where (\nabla^2 V) is the Laplacian of an unknown function (V), and (f) is a known function.1

This equation is widely applicable in physics, particularly in problems involving electrical, magnetic, and gravitational potentials, as well as in steady-state temperatures and fluid dynamics. The mathematician Siméon-Denis Poisson, for whom the equation is named, also developed the Poisson distribution, a statistical function used to describe events with low probabilities of occurrence within a specific time or space.123