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Solving Poisson's equation with fixed potential values on the boundary. Example: Laplace's equation with specified potentials at the borders of a metallic box.

Solving Poisson's equation with specified electric field (derivative of potential) on the boundary. Example: A charged plate with a constant electric field at the edge.

Solving Poisson's equation with a combination of Dirichlet and Neumann conditions. Example: A thermal problem with fixed temperature (Dirichlet) at one boundary and insulated (Neumann) at another.

Solving Poisson's equation with a linear combination of potential and its derivative specified at the boundary. Example: Heat transfer problem with convective cooling at the surface.

Solving Poisson's equation on a domain where opposite edges have the same potential. Example: Electric potential in a model of crystalline structure with repeating units.

Solving Poisson's equation with prescribed values of the function and its derivative at a specific point. Example: Fluid flow velocity and acceleration at an inlet.

Solving Poisson's equation when the boundary conditions are functions of position or time. Example: Temperature distribution with a time-varying boundary heat source.