Numerical solution of nonlinear fredholm integro-differential equations using spectral homotopy analysis method

Spectral homotopy analysis method (SHAM) as a modification of homotopy analysis method (HAM) is applied to obtain solution of high-order nonlinear Fredholm integro-differential problems. The existence and uniqueness of the solution and convergence of the proposed method are proved. Some examples are...

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Main Authors: Atabakan, Z. Pashazadeh, Nasab, A. Kazemi, Kilicman, Adem, Eshkuvatov, Zainidin K.
Format: Article
Language:English
Published: Hindawi Publishing Corporation 2013
Online Access:http://psasir.upm.edu.my/id/eprint/30127/
http://psasir.upm.edu.my/id/eprint/30127/1/Numerical%20solution%20of%20nonlinear%20fredholm%20integro.pdf
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author Atabakan, Z. Pashazadeh
Nasab, A. Kazemi
Kilicman, Adem
Eshkuvatov, Zainidin K.
author_facet Atabakan, Z. Pashazadeh
Nasab, A. Kazemi
Kilicman, Adem
Eshkuvatov, Zainidin K.
author_sort Atabakan, Z. Pashazadeh
building UPM Institutional Repository
collection Online Access
description Spectral homotopy analysis method (SHAM) as a modification of homotopy analysis method (HAM) is applied to obtain solution of high-order nonlinear Fredholm integro-differential problems. The existence and uniqueness of the solution and convergence of the proposed method are proved. Some examples are given to approve the efficiency and the accuracy of the proposed method. The SHAM results show that the proposed approach is quite reasonable when compared to homotopy analysis method, Lagrange interpolation solutions, and exact solutions.
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institution Universiti Putra Malaysia
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language English
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publishDate 2013
publisher Hindawi Publishing Corporation
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spelling upm-301272016-02-12T08:39:20Z http://psasir.upm.edu.my/id/eprint/30127/ Numerical solution of nonlinear fredholm integro-differential equations using spectral homotopy analysis method Atabakan, Z. Pashazadeh Nasab, A. Kazemi Kilicman, Adem Eshkuvatov, Zainidin K. Spectral homotopy analysis method (SHAM) as a modification of homotopy analysis method (HAM) is applied to obtain solution of high-order nonlinear Fredholm integro-differential problems. The existence and uniqueness of the solution and convergence of the proposed method are proved. Some examples are given to approve the efficiency and the accuracy of the proposed method. The SHAM results show that the proposed approach is quite reasonable when compared to homotopy analysis method, Lagrange interpolation solutions, and exact solutions. Hindawi Publishing Corporation 2013 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/30127/1/Numerical%20solution%20of%20nonlinear%20fredholm%20integro.pdf Atabakan, Z. Pashazadeh and Nasab, A. Kazemi and Kilicman, Adem and Eshkuvatov, Zainidin K. (2013) Numerical solution of nonlinear fredholm integro-differential equations using spectral homotopy analysis method. Mathematical Problems in Engineering, 2013. art. no. 674364. pp. 1-9. ISSN 1024-123X http://dx.doi.org/10.1155/2013/674364 10.1155/2013/674364
spellingShingle Atabakan, Z. Pashazadeh
Nasab, A. Kazemi
Kilicman, Adem
Eshkuvatov, Zainidin K.
Numerical solution of nonlinear fredholm integro-differential equations using spectral homotopy analysis method
title Numerical solution of nonlinear fredholm integro-differential equations using spectral homotopy analysis method
title_full Numerical solution of nonlinear fredholm integro-differential equations using spectral homotopy analysis method
title_fullStr Numerical solution of nonlinear fredholm integro-differential equations using spectral homotopy analysis method
title_full_unstemmed Numerical solution of nonlinear fredholm integro-differential equations using spectral homotopy analysis method
title_short Numerical solution of nonlinear fredholm integro-differential equations using spectral homotopy analysis method
title_sort numerical solution of nonlinear fredholm integro-differential equations using spectral homotopy analysis method
url http://psasir.upm.edu.my/id/eprint/30127/
http://psasir.upm.edu.my/id/eprint/30127/
http://psasir.upm.edu.my/id/eprint/30127/
http://psasir.upm.edu.my/id/eprint/30127/1/Numerical%20solution%20of%20nonlinear%20fredholm%20integro.pdf