An Iterative Approximate Method for Solving 2D Weakly Singular Fredholm Integral Equations of the Second Kind

This work aims to propose an iterative method for approximating solutions of two-dimensional weakly singular Fredholm integral Equation (2D-WSFIE) by incorporating the product integration technique, an appropriate cubature formula, and the Picard algorithm. This iterative approach is utilized to app...

Full description

Saved in:
Bibliographic Details
Main Authors: Mohamed I. Youssef, Mohamed A. Abdou, Abdulmalik Gharbi
Format: Article
Language:English
Published: MDPI AG 2025-06-01
Series:Mathematics
Subjects:
Online Access:https://www.mdpi.com/2227-7390/13/11/1854
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:This work aims to propose an iterative method for approximating solutions of two-dimensional weakly singular Fredholm integral Equation (2D-WSFIE) by incorporating the product integration technique, an appropriate cubature formula, and the Picard algorithm. This iterative approach is utilized to approximate the solution of the 2D-WSFIE that arises in some contact problems in linear elasticity. Under some sufficient conditions, the existence and uniqueness of the solution are established, an error bound for the approximate solution is estimated, and the order of convergence of the proposed algorithm is discussed. The effectiveness of the proposed method is illustrated through its application to some contact problems involving weakly singular kernels.
ISSN:2227-7390