Laplace’s and Poisson’s Equations in a Semi-Disc under the Dirichlet-Neumann Mixed Boundary Condition

ABSTRACT

In this work, the solution of Poisson’s equation in a semi-disc under a Dirichlet boundary condition at the base and a Neumann boundary condition on the circumference is calculated. The solution is determined in terms of Green’s function, which is calculated in two ways, by the method of images and by solving its equation. In the particular case of Laplace’s equation, it is presented a second way to solve it, which uses separation of variables and a Fourier transform.

KEYWORDS:
Laplace; Poisson; semi-disc; Dirichlet; Neumann; Green’s; images