Numerical solution of Laplace's equation for axially symmetric regions with a discontinuous linear boundary

Abstract

The solution of Laplace's equation for regions with axial symmetry is presented in this paper. The solution of the boundary-value problem is introduced as the potential of a single layer. Such an approach, in combination with the spline-approximation, allows us to introduce the solution of the integral equation as a system of linear algebraic equation. Examples of the solution of Laplace's equation for axially symmetric regions with a discontinuous linear boundary are given.