Research Article Open Access

On the General Solution of First-Kind Hypersingular Integral Equations

Suzan J. Obaiys1, Z. Abbas1, N. M.A. Nik Long1, A. F. Ahmad1, A. Ahmedov1 and Haider Khaleel Raad2
  • 1 Universiti Putra Malaysia, Malaysia
  • 2 Xavier University, United States
American Journal of Engineering and Applied Sciences
Volume 9 No. 2, 2016, 195-201

DOI: https://doi.org/10.3844/ajeassp.2016.195.201

Submitted On: 10 November 2015 Published On: 28 January 2016

How to Cite: Obaiys, S. J., Abbas, Z., Long, N. M. N., Ahmad, A. F., Ahmedov, A. & Raad, H. K. (2016). On the General Solution of First-Kind Hypersingular Integral Equations. American Journal of Engineering and Applied Sciences, 9(2), 195-201. https://doi.org/10.3844/ajeassp.2016.195.201

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 Hölder-continuous first derivative. Such equations are particularly important inmany physics and engineering problems, such as fracture mechanics, acoustics and elasticity.

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Keywords

  • HSIE
  • Singular Integrals
  • Fredholm Integral Equation
  • Chebyshev Polynomials