BEM for nonlinear boundary valve problems using an auxiliary boundary integral equation

Abstract

A nonlinear boundary value problem (BVP) governed by Laplace``s equation is considered. This thesis is considered with the numerical scheme for solving a nonlinear boundary integral equation (BIE) obtained by reformulating the nonlinear BVP. We give a simple alternative to the standard collocation method for the nonlinear BIE which is very computaionally easy. This method consists of one conventional linear system and another coupled linear system made up using an auxiliary BIE which is obtained by differentiating both side of the nonlinear BIE. We obtain the superconvergence of approximate solutions obtained by the method introduced in this thesis.