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Application of Homotopy Analysis Method to Fredholm and Volterra integral equations

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Author(s): S. Vahdati | Zulkifly Abbas | M. Ghasemi

Journal: Mathematical Sciences Quarterly Journal
ISSN 2008-1359

Volume: 4;
Issue: 3;
Start page: 267;
Date: 2010;
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Keywords: Homotopy Analysis Method | Homotopy Perturbation Method | Fredholm integral equations | Volterra integral equations.

ABSTRACT
Homotopy Analysis Method (HAM) and Homotopy Perturbation Method (HPM) are two analytic methods to solve the linear and nonlinear equations which can be used to obtain the numerical solution. This paper presents the application of the HAM to Fredholm and Volterra integral equations. The HAM contains the auxiliary parameter $hbar$, that provides a powerful tool to analyze strongly linear and nonlinear problems. Examples are provided to demonstrate the advantages of HAM over the HPM.