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Modified homotopy perturbation method for integro-differential and hypersingular integral equations

Homotopy perturbation method (HPM) is implemented to solve the mathematical problems. The solution is obtained by taking the summation of infinite series. This thesis present a modification of HPM by equating the second series as zero. Convergence and error estimation of HPM and modified HPM (MHP...

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Main Author: Zulkarnain, Fatimah Samihah
Format: Thesis
Language:English
Published: 2018
Subjects:
Mathematics
Homotopy equivalences
Online Access:http://psasir.upm.edu.my/id/eprint/83565/1/FS%202018%20100%20-%20ir.pdf
http://psasir.upm.edu.my/id/eprint/83565/
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spelling my.upm.eprints.835652022-01-06T03:18:59Z http://psasir.upm.edu.my/id/eprint/83565/ Modified homotopy perturbation method for integro-differential and hypersingular integral equations Zulkarnain, Fatimah Samihah Homotopy perturbation method (HPM) is implemented to solve the mathematical problems. The solution is obtained by taking the summation of infinite series. This thesis present a modification of HPM by equating the second series as zero. Convergence and error estimation of HPM and modified HPM (MHPM) are obtained in the class of C[a;b] for Fredholm-Volterra integral equation (FVIE) problem and Ck(D) where D is a closed subspace of R2 for higher order FVIDE problem. Many researchers solved singular integral equation with kernel equal to one. This study describes the implementation of HPM and MHPM on HSIE of the first kind with kernel is a constant on a diagonal. Convergence and error estimation are obtained in the class of Lr [-1;1]. MHPM is also used to solve HSIE of the second kind. For all cases, numerical examples are provided to exhibit the efficiency of the methods. The results obtained are more accurate than the previous works. 2018-04 Thesis NonPeerReviewed text en http://psasir.upm.edu.my/id/eprint/83565/1/FS%202018%20100%20-%20ir.pdf Zulkarnain, Fatimah Samihah (2018) Modified homotopy perturbation method for integro-differential and hypersingular integral equations. Doctoral thesis, Universiti Putra Malaysia. Mathematics Homotopy equivalences
institution Universiti Putra Malaysia
building UPM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Putra Malaysia
content_source UPM Institutional Repository
url_provider http://psasir.upm.edu.my/
language English
topic Mathematics
Homotopy equivalences
spellingShingle Mathematics
Homotopy equivalences
Zulkarnain, Fatimah Samihah
Modified homotopy perturbation method for integro-differential and hypersingular integral equations
description Homotopy perturbation method (HPM) is implemented to solve the mathematical problems. The solution is obtained by taking the summation of infinite series. This thesis present a modification of HPM by equating the second series as zero. Convergence and error estimation of HPM and modified HPM (MHPM) are obtained in the class of C[a;b] for Fredholm-Volterra integral equation (FVIE) problem and Ck(D) where D is a closed subspace of R2 for higher order FVIDE problem. Many researchers solved singular integral equation with kernel equal to one. This study describes the implementation of HPM and MHPM on HSIE of the first kind with kernel is a constant on a diagonal. Convergence and error estimation are obtained in the class of Lr [-1;1]. MHPM is also used to solve HSIE of the second kind. For all cases, numerical examples are provided to exhibit the efficiency of the methods. The results obtained are more accurate than the previous works.
format Thesis
author Zulkarnain, Fatimah Samihah
author_facet Zulkarnain, Fatimah Samihah
author_sort Zulkarnain, Fatimah Samihah
title Modified homotopy perturbation method for integro-differential and hypersingular integral equations
title_short Modified homotopy perturbation method for integro-differential and hypersingular integral equations
title_full Modified homotopy perturbation method for integro-differential and hypersingular integral equations
title_fullStr Modified homotopy perturbation method for integro-differential and hypersingular integral equations
title_full_unstemmed Modified homotopy perturbation method for integro-differential and hypersingular integral equations
title_sort modified homotopy perturbation method for integro-differential and hypersingular integral equations
publishDate 2018
url http://psasir.upm.edu.my/id/eprint/83565/1/FS%202018%20100%20-%20ir.pdf
http://psasir.upm.edu.my/id/eprint/83565/
_version_ 1724075396621664256
score 13.244404

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