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

Mohamed I. Youssef (), Mohamed A. Abdou and Abdulmalik Gharbi
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Mohamed I. Youssef: Department of Mathematics, Faculty of Science, Jouf University, Sakaka P.O. Box 2014, Saudi Arabia
Mohamed A. Abdou: Department of Mathematics, Faculty of Education, Alexandria University, Chatby, Alexandria 21526, Egypt
Abdulmalik Gharbi: Department of Mathematics, Faculty of Science, Jouf University, Sakaka P.O. Box 2014, Saudi Arabia

Mathematics, 2025, vol. 13, issue 11, 1-20

Abstract: 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.

Keywords: existence; uniqueness; 2D-weakly singular Fredholm integral equation; product integration technique; Picard algorithm; contact problems (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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