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

Document Type : Research Paper

Authors

Ibrahim Qadr Salim ¹

Younis A. Sabawi ²

Mohammad Sh. Hasso ³

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

10.32894/kujss.2025.161871.1222

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

Subjects