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

International Journal of Mathematical Modelling & Computations

دوره 13، 1 (WINTER) - شماره پیاپی 49، خرداد 2023

نوع مقاله: Full Length Article

شناسه دیجیتال (DOI): 10.30495/ijm2c.2023.1960582.1254

نویسندگان

Maryam Mohammadi¹؛ A. Zakeri^{* 2}؛ Majid Karami³؛ Narges Taheri³؛ Raheleh Nouraei³

¹Islamic Azad University, South Tehran Branch, Tehran

²Khajeh Nasir Toosi University of Technology

³Islamic Azad University, South Tehran Branch

چکیده

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.

کلیدواژه‌ها

Fredholm integral equations؛ Collocation method؛ Bivariate hybrid block-pulse functions؛ Normalized Bernstein polynomials؛ Convergence analysis