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

Document Type : Research Paper

Authors

1 Department of Mathematics, Faculty of Science and Health, Koya University, Koya, Kurdistan Region-F.R. Iraq

2 Department of Mathematics, Faculty of Science and Health, Koya University, Koya , Erbil, Iraq

3 Department 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.

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Kirkuk Journal of Science
Volume 20, Issue 3
September 2025
Page 55-65

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History

  • Receive Date: 22 June 2025
  • Revise Date: 07 August 2025
  • Accept Date: 12 August 2025

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