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.