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

Subject Areas : International Journal of Mathematical Modelling & Computations

Jafar Khazaian ¹ , Nouredin Parandin ² , Farajollah Mohammadi Yaghoobi ³ , Nasrin Karami Kabir ⁴

1 - Department of Mathematics, Hamedan Branch, Islamic Azad University, Hamedan, Iran.
2 - Department of Mathematics Kermanshah Branch, Islamic Azad University, Kermanshah, Iran
3 - Department of Mathematics Hamedan Branch, Islamic Azad University Hamedan, Iran.
4 - Department of Mathematics, Hamedan Branch, Islamic Azad University, Hamedan, Iran.

Received: 2021-03-02 Accepted : 2022-02-08 Published : 2022-03-30

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

Abstract :

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.