A Numerical Solution for 2D-Nonlinear Fredholm Integral Equations Based on Hybrid Functions Basis

Subject Areas : International Journal of Mathematical Modelling & Computations

Maryam Mohammadi ¹ (Islamic Azad University, South Tehran Branch, Tehran)
A. Zakeri ² (Khajeh Nasir Toosi University of Technology)
Majid Karami ³ (Islamic Azad University, South Tehran Branch)
Narges Taheri ⁴ (Islamic Azad University, South Tehran Branch)
Raheleh Nouraei ⁵ (Islamic Azad University, South Tehran Branch)

Received: 2022-06-08 Accepted : 2023-04-02 Published : 2023-03-01

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

Abstract :

This work considers a numerical method based on the 2D-hybrid block-pulse functions and normalized Bernstein polynomials to solve 2D-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.