A new generalized definition of singular kernel for two-dimensional Fredholm integral equation

This paper proposes a new generalized definition of singular kernel for TwoDimensional Fredholm integral equation (T-DFIE). Furthermore, this integral equation can be solved by using two different methods. These methods are Toeplitz matrix method (TMM) and Product Nyström method (PNM). Moreover, numerical examples are considered when the generalized kernel takes the following forms: Carleman function, logarithmic form, and Cauchy kernel. The given numerical examples showed the efficiency and accuracy of the introduced methods.

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