Abstract
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 Nystrom 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.
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