Solving mixed boundary value problem VIA an integral equation with the generalized neumann kernel in bounded doubly connected region

Abstract

This dissertation determines solution of a certain class of a mixed boundary value problem in bounded doubly connected region by using the method of boundary integral equations. The method depends on reformulating the boundary value problem with mixed Dirichlet - Neumann condition to the Riemann - Hilbert problem. Our approach in this dissertation is to work out in detail the reformulation of the mixed boundary value problem into the Riemann - Hilbert problem and study the efficiency of the proposed numerical scheme on challenging geometries, in particular when the boundaries are closed to each other. As an examination of the proposed method, some numerical examples for some different test regions are presented. These examples include comparison between the numerical result and the exact solutions. Numerical examples reveal that the proposed method offers an effective solution technique for the mixed boundary value problem when the boundaries are close to each other.