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

International Journal of Mathematical Modelling & Computations

مقاله 1، دوره 12، 1 (WINTER) - شماره پیاپی 45، خرداد 2022، صفحه 1-14   

نوع مقاله: Full Length Article

شناسه دیجیتال (DOI): 10.30495/ijm2c.2022.688969

نویسندگان

Jafar Khazaian¹؛ Nouredin Parandin^{* 2}؛ Farajollah Mohammadi Yaghoobi³؛ Nasrin Karami Kabir¹

¹Department of Mathematics, Hamedan Branch, Islamic Azad University, Hamedan, Iran.

²Department of Mathematics Kermanshah Branch, Islamic Azad University, Kermanshah, Iran

³Department of Mathematics Hamedan Branch, Islamic Azad University Hamedan, Iran.

چکیده

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.

کلیدواژه‌ها

Volterra-Fredholm integral equations؛ Block-pulse functions؛ Operational matrix؛ Legendre polynomials