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On the general solution of first-kind hypersingular integral equations

A new algorithm is presented to provide a general solution for a first type Hyper singular Integral Equation (HSIE). The singular integral has been converted into a regular form by cancelling the singularity and then transforming it into a system of algebraic equation based orthogonal poly- nomials....

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Main Authors: Obaiys, Suzan Jabbar, Abbas, Zulkifly, Nik Long, Nik Mohd Asri, Ahmad, Ahmad Fahad, Ahmedov, Anvarjon, Raad, Haider Khaleel
Format: Article
Language:English
Published: Science Publications 2016
Online Access:http://psasir.upm.edu.my/id/eprint/53431/1/On%20the%20general%20solution%20of%20first-kind%20Hypersingular%20Integr.pdf
http://psasir.upm.edu.my/id/eprint/53431/
http://thescipub.com/abstract/10.3844/ajeassp.2016.195.201
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spelling my.upm.eprints.534312017-12-04T09:27:48Z http://psasir.upm.edu.my/id/eprint/53431/ On the general solution of first-kind hypersingular integral equations Obaiys, Suzan Jabbar Abbas, Zulkifly Nik Long, Nik Mohd Asri Ahmad, Ahmad Fahad Ahmedov, Anvarjon Raad, Haider Khaleel A new algorithm is presented to provide a general solution for a first type Hyper singular Integral Equation (HSIE). The singular integral has been converted into a regular form by cancelling the singularity and then transforming it into a system of algebraic equation based orthogonal poly- nomials. We applied the convergence method presented by (Obaiys, 2013) to conform the numerical solution of the regularized Hadamard equation, which has shown an absolute agreement with the exact solution within small values of n. The proposed method has been examined by various HSIEs where the displacement function satisfies the HÓ§lder-continuous first derivative. Such equations are particularly important inmany physics and engineering problems, such as fracture mechanics, acoustics and elasticity. Science Publications 2016 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/53431/1/On%20the%20general%20solution%20of%20first-kind%20Hypersingular%20Integr.pdf Obaiys, Suzan Jabbar and Abbas, Zulkifly and Nik Long, Nik Mohd Asri and Ahmad, Ahmad Fahad and Ahmedov, Anvarjon and Raad, Haider Khaleel (2016) On the general solution of first-kind hypersingular integral equations. American Journal of Engineering and Applied Sciences, 9 (2). pp. 195-201. ISSN 1941-7020; ESSN: 1941-7039 http://thescipub.com/abstract/10.3844/ajeassp.2016.195.201 10.3844/ajeassp.2016.195.201
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
description A new algorithm is presented to provide a general solution for a first type Hyper singular Integral Equation (HSIE). The singular integral has been converted into a regular form by cancelling the singularity and then transforming it into a system of algebraic equation based orthogonal poly- nomials. We applied the convergence method presented by (Obaiys, 2013) to conform the numerical solution of the regularized Hadamard equation, which has shown an absolute agreement with the exact solution within small values of n. The proposed method has been examined by various HSIEs where the displacement function satisfies the HÓ§lder-continuous first derivative. Such equations are particularly important inmany physics and engineering problems, such as fracture mechanics, acoustics and elasticity.
format Article
author Obaiys, Suzan Jabbar
Abbas, Zulkifly
Nik Long, Nik Mohd Asri
Ahmad, Ahmad Fahad
Ahmedov, Anvarjon
Raad, Haider Khaleel
spellingShingle Obaiys, Suzan Jabbar
Abbas, Zulkifly
Nik Long, Nik Mohd Asri
Ahmad, Ahmad Fahad
Ahmedov, Anvarjon
Raad, Haider Khaleel
On the general solution of first-kind hypersingular integral equations
author_facet Obaiys, Suzan Jabbar
Abbas, Zulkifly
Nik Long, Nik Mohd Asri
Ahmad, Ahmad Fahad
Ahmedov, Anvarjon
Raad, Haider Khaleel
author_sort Obaiys, Suzan Jabbar
title On the general solution of first-kind hypersingular integral equations
title_short On the general solution of first-kind hypersingular integral equations
title_full On the general solution of first-kind hypersingular integral equations
title_fullStr On the general solution of first-kind hypersingular integral equations
title_full_unstemmed On the general solution of first-kind hypersingular integral equations
title_sort on the general solution of first-kind hypersingular integral equations
publisher Science Publications
publishDate 2016
url http://psasir.upm.edu.my/id/eprint/53431/1/On%20the%20general%20solution%20of%20first-kind%20Hypersingular%20Integr.pdf
http://psasir.upm.edu.my/id/eprint/53431/
http://thescipub.com/abstract/10.3844/ajeassp.2016.195.201
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score 13.211869

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