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Math. Comput. Appl. 2016, 21(2), 9; doi:10.3390/mca21020009

The Regularization-Homotopy Method for the Two-Dimensional Fredholm Integral Equations of the First Kind

Department of Mathematics, Amasya University, Ipekkoy, Amasya 05000, Turkey
Academic Editor: Fazal M. Mahomed
Received: 24 February 2016 / Revised: 18 March 2016 / Accepted: 22 March 2016 / Published: 30 March 2016
View Full-Text   |   Download PDF [227 KB, uploaded 30 March 2016]

Abstract

In this work, we consider two-dimensional linear and nonlinear Fredholm integral equations of the first kind. The combination of the regularization method and the homotopy perturbation method, or shortly, the regularization-homotopy method is used to find a solution to the equation. The application of this method is based upon converting the first kind of equation to the second kind by applying the regularization method. Then the homotopy perturbation method is employed to the resulting second kind of equation to obtain a solution. A few examples including linear and nonlinear equations are provided to show the validity and applicability of this approach. View Full-Text
Keywords: Fredholm integral equations; regularization method; homotopy perturbation method; 45A05; 65R20; 65J20 Fredholm integral equations; regularization method; homotopy perturbation method; 45A05; 65R20; 65J20
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. (CC BY 4.0).

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MDPI and ACS Style

Altürk, A. The Regularization-Homotopy Method for the Two-Dimensional Fredholm Integral Equations of the First Kind. Math. Comput. Appl. 2016, 21, 9.

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