PoissonGleichungssystem
The Poisson equation is a second-order partial differential equation that arises in various fields of physics and engineering, including electrostatics, fluid dynamics, and heat transfer. It is named after the French mathematician Siméon Denis Poisson. The Poisson equation in its most general form is given by:
∇²φ = f
where ∇² is the Laplacian operator, φ is the unknown function, and f is a given function. The
∇²φ = ∂²φ/∂x² + ∂²φ/∂y² + ∂²φ/∂z²
In the context of electrostatics, the Poisson equation describes the relationship between the electric potential φ and
∇²φ = -ρ/ε₀
The Poisson equation can be solved using various methods, including analytical solutions, numerical methods, and Green's