Iterative solution of linear and nonlinear boundary problems using PIES

Abstract

The paper presents an effective approach to solving boundary problems modeled by a nonlinear partial differential equation. An applied algorithm bases on: an iterative method used in order to find successive approximations to the solution of a boundary problem and PIES method as a tool for solving a boundary problem in each iteration step. The paper also contains some suggestions about an effective way of domains modeling and calculation of integrals over those domains. Authors also have performed an initial verification of a method on the basis of a linear equation and nonlinear equations with a various intensity of nonlinearity. © 2010 Springer-Verlag Berlin Heidelberg.