Boundary Contraction Solution of Laplace's Differential Equation II

Abstract

In this paper the numerical solution of Laplace's equation for the circle is discussed and consideration is given to the convergence of the solution obtained by the boundary contraction method to the analytic solution. It is proved that in order to achieve this a relation between the mesh sizes in the circumferential and radial direction must exist. It is also demonstrated that the error due to the contraction of boundaries can be made insignificant.