Numerical Treatments of Functional Fredholm Integral Equation in 2D with Discontinuous Kernels

Abstract

This work proposes a new definition of the functional Fredholm integral equation in 2D of the second kind with discontinuous kernels (FT-DFIE). Furthermore, the work is concerned to study this new equation numerically. The existence of a unique solution of the equation is proved. In addition, the approximate solutions are obtained by two powerful methods Toeplitz Matrix Method (TMM) and Product Nyström Methods (PNM). The given numerical examples showed the efficiency and accuracy of the introduced methods.