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Application of Homotopy Analysis Method for Solving Systems of Volterra Integral Equations

Published online by Cambridge University Press:  03 June 2015

M. Matinfar ,
M. Saeidy  and
J. Vahidi
M. Matinfar*
Affiliation:
Department of Mathematics and Computer Science, University of Mazandaran, Babolsar, Iran
M. Saeidy*
Affiliation:
Department of Mathematics and Computer Science, University of Mazandaran, Babolsar, Iran
J. Vahidi*
Affiliation:
Department of Mathematics, Iran University of Science and Technology, Behshahr, Iran
*
Corresponding author. Email: M.Matinfar@umz.ac.ir
Email: M.Saidy@umz.ac.ir
Email: J.Vahidi@umz.ac.ir
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Abstract

In this paper, we prove the convergence of homotopy analysis method (HAM). We also apply the homotopy analysis method to obtain approximate analytical solutions of systems of the second kind Volterra integral equations. The HAM solutions contain an auxiliary parameter which provides a convenient way of controlling the convergence region of series solutions. It is shown that the solutions obtained by the homotopy-perturbation method (HPM) are only special cases of the HAM solutions. Several examples are given to illustrate the efficiency and implementation of the method.

Keywords

54A4026E50Homotopy analysis methodhomotopy perturbation methodsystems of Volterra integral equations
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 4 , Issue 1 , February 2012 , pp. 36 - 45
Copyright
Copyright © Global-Science Press 2012

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