Approximate Solutions to Weakly Singular Fredholm Integral Equations of the Second Kind using Shifted Legendre Polynomials of the First Kind

Authors

  • Emil Sobhi Shoukralla Faculty of Electronic, Menoufiya University, Menofia Governorate 6131567, Egypt
  • Alfaisal Abdelhamid Hasan Basic and Sciences Department, College of Engineering and Technology, Arab Academy for Science, Technology & Maritime Transport, Aswan Governorate 1241502, Egypt
  • Sara Abdelhamid Basic and Sciences Department, College of Engineering and Technology, Arab Academy for Science, Technology & Maritime Transport, Aswan Governorate 1241502, Egypt
  • Ahmed Yehia Sayed Physics and Engineering Mathematics Department, Faculty of Engineering Helwan University Mataria Branch, Cairo Governorate, Egypt

DOI:

https://doi.org/10.37934/araset.50.2.7689

Keywords:

Fredholm integral equations, weakly singular kernels, Legendre polynomials, approximation, computational method

Abstract

In this research, we presented a simple approach to approximate the second type of linear weakly singular and non-singular Fredholm integral. Shifted Legendre polynomials of the first kind in matrix-vector forms were used to construct the approach. The singularity of the kernel was removed analytically. Theorems regarding the convergence of the estimations of the error norm and the mean were proved. The numerical examples demonstrated the method's uniqueness and precision.

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Author Biographies

Emil Sobhi Shoukralla, Faculty of Electronic, Menoufiya University, Menofia Governorate 6131567, Egypt

shoukralla@el-eng.menofia.edu.eg

Alfaisal Abdelhamid Hasan, Basic and Sciences Department, College of Engineering and Technology, Arab Academy for Science, Technology & Maritime Transport, Aswan Governorate 1241502, Egypt

alfaisal772001@aast.edu

Sara Abdelhamid, Basic and Sciences Department, College of Engineering and Technology, Arab Academy for Science, Technology & Maritime Transport, Aswan Governorate 1241502, Egypt

saraD01292@m-eng.helwan.edu.eg

Ahmed Yehia Sayed, Physics and Engineering Mathematics Department, Faculty of Engineering Helwan University Mataria Branch, Cairo Governorate, Egypt

AHMED_BADR@m-eng.helwan.edu.eg

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Published

2024-08-25

How to Cite

Shoukralla, E. S., Hasan, A. A., Abdelhamid, S., & Sayed, A. Y. (2024). Approximate Solutions to Weakly Singular Fredholm Integral Equations of the Second Kind using Shifted Legendre Polynomials of the First Kind. Journal of Advanced Research in Applied Sciences and Engineering Technology, 50(2), 76–89. https://doi.org/10.37934/araset.50.2.7689

Issue

Vol. 50 No. 2: August (2025)

Section

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