American Journal of Engineering and Applied Sciences

On the General Solution of First-Kind Hypersingular Integral Equations

Suzan J. Obaiys, Z. Abbas, N. M.A. Nik Long, A. F. Ahmad, A. Ahmedov and Haider Khaleel Raad

DOI : 10.3844/ajeassp.2016.195.201

American Journal of Engineering and Applied Sciences

Volume 9, Issue 2

Pages 195-201

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.

Copyright

© 2016 Suzan J. Obaiys, Z. Abbas, N. M.A. Nik Long, A. F. Ahmad, A. Ahmedov and Haider Khaleel Raad. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.