Error Analysis for Numerical Solutions of Hammerstein Integral Equation With A Generalized Singular Kernel

A. M. Al-Bugami

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Error Analysis for Numerical Solutions of Hammerstein Integral Equation With A Generalized Singular Kernel

机译：具有广义奇异核的Hammerstein积分方程数值解的误差分析

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In this work, the existence and uniqueness solution of the Hammerstein integral equation (HIE), with a generalized singular kernel, is discussed and solved numerically using Toeplitz matrix method and Product Nystr?m method. Moreover, the error analysis for these methods is discussed. Finally, numerical results when the kernel takes a generalized logarithmic form, Carleman function and Cauchy kernel function are investigated. Also the error, in each case, is estimated.

机译：在这项工作中，讨论了具有广义奇异核的Hammerstein积分方程（HIE）的存在和唯一解，并使用Toeplitz矩阵法和乘积Nystr？m方法进行了数值求解。此外，讨论了这些方法的误差分析。最后，研究了当核采用广义对数形式，Carleman函数和Cauchy核函数时的数值结果。此外，在每种情况下，都会估算误差。

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《Progress in Applied Mathematics》 |2013年第2期|共15页
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A. M. Al-Bugami;
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中图分类数学;
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2. Error analysis of Jacobi spectral collocation methods for Fredholm-Hammerstein integral equations with weakly singular kernel [J] . Panigrahi Bijaya Laxmi International journal of computer mathematics . 2019,第5a8期

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机译：弗雷霍尔姆 - Hammerstein整体方程与弱奇异内核的误差分析
4. FREDHOLM-VOLTERRA INTEGRAL EQUATION WITH A GENERALIZED SINGULAR KERNEL AND ITS NUMERICAL SOLUTIONS [C] . I. L. El-Kalla, A. M. Al-Bugami International Conference on Mathematical Science . 2011

机译：Fredholm-Volterra积分方程，具有通用奇异内核及其数值解决方案
5. Numerical solution of integral equations with nonsmooth kernel and applications. [D] . Kang, Sheon Young. 2000

机译：具有非光滑核的积分方程的数值解及其应用。
6. Reliable and efficient a posteriori error estimation for adaptive IGA boundary element methods for weakly-singular integral equations [O] . Michael Feischl, Gregor Gantner, Dirk Praetorius -1

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7. FREDHOLM-VOLTERRA INTEGRAL EQUATION WITH A GENERALIZED SINGULAR KERNEL AND ITS NUMERICAL SOLUTIONS [O] . I.L. El-Kalla, A.M. Al-Bugami 2011

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8. Multiquadric collocation methods in the numerical solution of Volterra integral equations with weakly singular kernels [R] . Makroglou, A, Kansa, E J 1993

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Error Analysis for Numerical Solutions of Hammerstein Integral Equation With A Generalized Singular Kernel

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