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Abstract and Applied Analysis
Volume 2014, Article ID 629179, 13 pages
Research Article

An Adaptive Approach to Solutions of Fredholm Integral Equations of the Second Kind

Department of Secondary Science and Mathematics Education, Muğla Sıtkı Koçman University, 48000 Muğla, Turkey

Received 5 May 2014; Revised 13 September 2014; Accepted 22 September 2014; Published 17 November 2014

Academic Editor: Chun-Gang Zhu

Copyright © 2014 Nebiye Korkmaz and Zekeriya Güney. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


As an approach to approximate solutions of Fredholm integral equations of the second kind, adaptive hp-refinement is used firstly together with Galerkin method and with Sloan iteration method which is applied to Galerkin method solution. The linear hat functions and modified integrated Legendre polynomials are used as basis functions for the approximations. The most appropriate refinement is determined by an optimization problem given by Demkowicz, 2007. During the calculations -projections of approximate solutions on four different meshes which could occur between coarse mesh and fine mesh are calculated. Depending on the error values, these procedures could be repeated consecutively or different meshes could be used in order to decrease the error values.