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On the general solution of first-kind hypersingular integral equations


Citation

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

Abstract

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.


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Additional Metadata

Item Type: Article
Divisions: Faculty of Science
Institute for Mathematical Research
DOI Number: https://doi.org/10.3844/ajeassp.2016.195.201
Publisher: Science Publications
Keywords: HSIE; Singular integrals; Fredholm integral equation; Chebyshev polynomials
Depositing User: Nurul Ainie Mokhtar
Date Deposited: 30 Oct 2017 08:29
Last Modified: 04 Dec 2017 09:27
Altmetrics: http://www.altmetric.com/details.php?domain=psasir.upm.edu.my&doi=10.3844/ajeassp.2016.195.201
URI: http://psasir.upm.edu.my/id/eprint/53431
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