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

A. M. Al-Bugami


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 Nyström 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.


Hammerstein singular integral equation; Toeplitz matrix; Product Nyström method; Logarithmic form; Carleman function

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