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; Haider Khaleel Raad

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On the General Solution of First-Kind Hypersingular Integral Equations

机译：一类超奇异积分方程的一般解

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

机译：提出了一种新算法，为第一类超奇异积分方程（HSIE）提供了通用的解决方案。通过消除奇点并将其转换为基于代数方程的正交多项式系统，将奇异积分转换为正则形式。我们使用（Obaiys，2013）提出的收敛方法来拟合正则化Hadamard方程的数值解，该方程表明在n的小值内与精确解绝对吻合。所提出的方法已由各种HSIE检验，其中位移函数满足H连续的一阶导数。这样的方程式在许多物理和工程问题中尤其重要，例如断裂力学，声学和弹性。

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来源
《American journal of engineering and applied sciences》 |2016年第2期|195-201|共7页
作者
Suzan J. Obaiys; Z. Abbas; N.M.A. Nik Long; A.F. Ahmad; A. Ahmedov; Haider Khaleel Raad;
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作者单位

Department of Physics, Universiti Putra Malaysia, Serdang, Malaysia;

Department of Physics, Universiti Putra Malaysia, Serdang, Malaysia;

Institute for Mathematical Research, Universiti Putra Malaysia, Serdang, Malaysia;

Institute for Mathematical Research, Universiti Putra Malaysia, Serdang, Malaysia;

Institute for Mathematical Research, Universiti Putra Malaysia, Serdang, Malaysia;

Department of Physics, Xavier University, Cincinnati, Ohio, USA;

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正文语种 eng
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关键词
HSIE; Singular Integrals; Fredholm Integral Equation; Chebyshev Polynomials;

机译：HSIE;奇异积分弗雷德霍尔姆积分方程;切比雪夫多项式;

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1. On the General Solution of First-Kind Hypersingular Integral Equations | Science Publications [J] . A. Ahmedov, A. F. Ahmad, Haider Khaleel Raad, American journal of engineering and applied sciences . 2016,第2期

机译：一类超奇异积分方程的一般解科学出版物
2. Nearly singular approximations of CPV integrals with end- and corner-singularities for the numerical solution of hypersingular boundary integral equations [J] . Hang Ma, Norio Kamiya Engineering analysis with boundary elements . 2003,第6期

机译：超奇异边界积分方程数值解的CPV积分具有奇异的端和角奇点近似
3. Some particular solutions for penny-shaped crack problem by sing hypersingular integral equation or differential-integral equation [J] . Y.Z.Chen, X.Y.Lin, Z.Q.Peng Archive of Applied Mechanics . 1998,第3a4期

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4. On Estimate of the Gradient of the Hypersingular Integral Equation Solution with use of Some Numerical Scheme [C] . Gleb V. Ryzhakov International Conference of Numerical Analysis and Applied Mathematics . 2014

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5. The solution of hypersingular integral equations with applications in acoustics and fracture mechanics [D] . St.John, Richard S. 1998

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6. Modified homotopy perturbation method for solving hypersingular integral equations of the first kind [O] . Z. K. Eshkuvatov, F. S. Zulkarnain, N. M. A. Nik Long, -1

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7. The numerical solution of first-kind logarithmic-kernel integral equations on smooth open arcs [O] . Kendall E. Atkinson, Ian H. Sloan 1991

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8. Solvability of a Class of Hypersingular Nonlinear Integral Equations [R] . Vavilov, S. A., Movchan, A. B., Zalipaev, V. V. 1994

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On the General Solution of First-Kind Hypersingular Integral Equations

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