Numerical Solution Two-Dimensional Volterra-Fredholm Integral Equations of the Second Kind with Block-Pulse Functions Based on Legendre Polynomials

الموضوعات : فصلنامه ریاضی

Jafar Khazaian ¹ (Department of Mathematics, Hamedan Branch, Islamic Azad University, Hamedan, Iran.)
Nouredin Parandin ² (Department of Mathematics Kermanshah Branch, Islamic Azad University, Kermanshah, Iran)
Farajollah Mohammadi Yaghoobi ³ (Department of Mathematics Hamedan Branch, Islamic Azad University Hamedan, Iran.)
Nasrin Karami Kabir ⁴ (Department of Mathematics, Hamedan Branch, Islamic Azad University, Hamedan, Iran.)

تاريخ الإرسال : 18 الثلاثاء , رجب, 1442 تاريخ التأكيد : 07 الثلاثاء , رجب, 1443 تاريخ الإصدار : 27 الأربعاء , شعبان, 1443

الکلمات المفتاحية: Volterra-Fredholm integral equations, Operational matrix, legendre polynomials, Block-pulse functions,

ملخص المقالة :

In this paper, we present a new numerical technique based on Block-pulse functions to solve two-dimensional Volterra-Fredholm integral equations of the second kind. To produce Block-pulse functions, the orthogonal Legendre polynomials is used. Furthermore, operational matrix is applied to convert two-dimensional Volterra-Fredholm integral equations to a linear algebraic system. The convergence analysis of the new method is discussed. Finally, some numerical examples are given to confirm the applicability and efficiency of the new method for solving two-dimensional Volterra-Fredholm integral equations of the second kind.