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

الموضوعات : فصلنامه ریاضی

Maryam Mohammadi ¹ , A. Zakeri ² , Majid Karami ³ , Narges Taheri ⁴ , Raheleh Nouraei ⁵

1 - Department of Mathematics, Islamic Azad University, South Tehran Branch, Tehran, Iran
2 - Faculty of Mathematics, K. N. Toosi University of Technology, Tehran, Iran
3 - Department of Mathematics, Islamic Azad University, South Tehran Branch, Tehran, Iran
4 - Department of Mathematics, Islamic Azad University, South Tehran Branch, Tehran, Iran
5 - Department of Mathematics, Islamic Azad University, South Tehran Branch, Tehran, Iran

تاريخ الإرسال : 09 الأربعاء , ذو القعدة, 1443 تاريخ التأكيد : 11 الأحد , رمضان, 1444 تاريخ الإصدار : 09 الأربعاء , شعبان, 1444

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

ملخص المقالة :

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.

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