On the General Solution of First-Kind Hypersingular Integral Equations
- 1 Universiti Putra Malaysia, Malaysia
- 2 Xavier University, United States
Copyright: © 2020 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.
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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- Singular Integrals
- Fredholm Integral Equation
- Chebyshev Polynomials