Resolvent Kernel and Haar Wavelet Techniques for Solving Coupled of Fredholm Integro-Differential Equations

Salim, Ibrahim Qadr; Sabawi, Younis A.; Hasso, Mohammad Sh.

doi:10.32894/kujss.2025.161871.1222

	Resolvent Kernel and Haar Wavelet Techniques for Solving Coupled of Fredholm Integro-Differential Equations
Kirkuk Journal of Science
Volume 20, Issue 3, September 2025, Pages 55-65 PDF (403.11 K)
Document Type: Research Paper
DOI: 10.32894/kujss.2025.161871.1222
Authors
Ibrahim Qadr Salim¹; Younis A. Sabawi^* ²; Mohammad Sh. Hasso³
¹Department of Mathematics, Faculty of Science and Health, Koya University, Koya, Kurdistan Region-F.R. Iraq
²Department of Mathematics, Faculty of Science and Health, Koya University, Koya , Erbil, Iraq
³Department of Mathematics, Faculty of Science and Health, Koya University, Koya KOYA45, Kurdistan Region-F.R. Iraq
Abstract
This study focuses on the Fredholm integro-differential equations and is frequently found in areas of applied mathematics, physics, and engineering fields. To address these systems and obtain exact of solutions under suitable conditions, we propose a novel analytical approach. We choose the Haar wavelet colocation method for processing due to its simplicity, effectiveness, and ability to handle non-smooth solutions. The integral terms in these equations are determined using the trapezoidal rule, which effectively strikes a balance between accuracy and computational efficiency. These results are compared with analytical solutions. The comparisons show that the suggested strategy yields highly accurate results and offers a solid framework for solving the Fredholm integro-differential equations.
Keywords
System of Fredholm integro-differential equations; Resolvent kernel; Haar wavelet method

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