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Volume 4, Issue 1
Application of Homotopy Analysis Method for Solving Systems of Volterra Integral Equations

M. Matinfar, M. Saeidy & J. Vahidi

DOI: 10.4208/aamm.10-m1143

Adv. Appl. Math. Mech., 4 (2012), pp. 36-45.

Published online: 2012-04

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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

Homotopy analysis method, homotopy perturbation method, systems of Volterra integral equations.

  • AMS Subject Headings

54A40, 26E50

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-4-36, author = {Matinfar , M.Saeidy , M. and Vahidi , J.}, title = {Application of Homotopy Analysis Method for Solving Systems of Volterra Integral Equations}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2012}, volume = {4}, number = {1}, pages = {36--45}, 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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.10-m1143}, url = {http://global-sci.org/intro/article_detail/aamm/105.html} }
TY - JOUR T1 - Application of Homotopy Analysis Method for Solving Systems of Volterra Integral Equations AU - Matinfar , M. AU - Saeidy , M. AU - Vahidi , J. JO - Advances in Applied Mathematics and Mechanics VL - 1 SP - 36 EP - 45 PY - 2012 DA - 2012/04 SN - 4 DO - http://doi.org/10.4208/aamm.10-m1143 UR - https://global-sci.org/intro/article_detail/aamm/105.html KW - Homotopy analysis method, homotopy perturbation method, systems of Volterra integral equations. AB -

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.

Matinfar , M.Saeidy , M. and Vahidi , J.. (2012). Application of Homotopy Analysis Method for Solving Systems of Volterra Integral Equations. Advances in Applied Mathematics and Mechanics. 4 (1). 36-45. doi:10.4208/aamm.10-m1143
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