2025, Vol. 6, Issue 1, Part C
Solving the Fredholm integral equation of the second kind with a weakly singular kernel using the collocation method
Author(s): Dheyaa Hamid Hatif AlKroosh
Abstract: Fredholm integral equations of the second kind with weakly singular kernels frequently arise in various scientific and engineering applications, including electrostatics, fluid mechanics, and wave propagation. These equations are often challenging to solve numerically due to the instability introduced by the singularity at . In this paper, we propose the use of the aggregation method for efficiently solving Fredholm integral equations with weakly singular kernels. The aggregation method addresses the singularity by discretizing the integral and applying specialized approximations in regions near the singularity, ensuring both stability and accuracy. We present a detailed formulation of the method, followed by numerical experiments to validate its performance. The results demonstrate that the aggregation method converges rapidly and maintains numerical stability, even for large grid sizes. A convergence study shows quadratic convergence as the grid is refined. Furthermore, the method is compared with traditional numerical techniques, such as Nyström and collocation methods, to highlight its advantages in terms of accuracy and computational efficiency. This study provides a reliable and efficient approach for solving weakly singular Fredholm integral equations, with potential applications in a variety of fields, including computational physics and engineering.
DOI: https://doi.org/10.22271/math.2025.v6.i1c.198
Pages: 219-231 | Views: 88 | Downloads: 46
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How to cite this article:
Dheyaa Hamid Hatif AlKroosh. Solving the Fredholm integral equation of the second kind with a weakly singular kernel using the collocation method. Journal of Mathematical Problems, Equations and Statistics. 2025; 6(1): 219-231. DOI: 10.22271/math.2025.v6.i1c.198
