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Abdou, M.A. and AL-Bugami, A.M. (2013) Nonlinear Fredholm-Volterra Integral Equation and Its Numerical Solutions with Quadrature Methods. Journal of Advances in Mathematics, 4, 415-422.

has been cited by the following article:

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

  AUTHORS: Abeer M. Al-Bugami

  KEYWORDS: Functional Integral Equation, TMM, PNM, Hammerstion

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.11 No.11, November 30, 2023

  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 Nystr?m Methods (PNM). The given numerical examples showed the efficiency and accuracy of the introduced methods.