Maryam Mohammadi - Islamic Azad University, South Tehran Branch, Tehran
A. Zakeri - Khajeh Nasir Toosi University of Technology
Majid Karami - Islamic Azad University, South Tehran Branch
Narges Taheri - Islamic Azad University, South Tehran Branch
Raheleh Nouraei - Islamic Azad University, South Tehran Branch

This work considers a numerical method based on the ۲D-hybrid block-pulse functions and normalized Bernstein polynomials to solve ۲D-nonlinear Fredholm integral equations of the second type. These problems are reduced to a system of nonlinear algebraic equations and solved by Newton's iterative method along with the numerical integration and collocation methods. Also, the convergence theorem for this algorithm is proved. Finally, some numerical examples are given to show the effectiveness and simplicity of the proposed method.

Fredholm integral equations, collocation method, Bivariate hybrid block-pulse functions, Normalized Bernstein polynomials, Convergence analysis