Enhanced Numerical Techniques for Selective Integration Using Error Correction Methods

Authors

Israa Essa Abed Department of Networks and Computer Software, Al-Furat Al-Awsat Technical University, Babylon, Iraq https://orcid.org/0009-0007-9619-6501
Wafaa M. R. Shakir Department of Networks and Computer Software, Al-Furat Al-Awsat Technical University, Babylon, Iraq https://orcid.org/0000-0002-8958-0261

DOI:

https://doi.org/10.30526/39.2.4304

Keywords:

Composite rules , Enhanced numerical , Error correction

Abstract

Classical numerical integration methods, such as Simpson’s rule and Gaussian quadrature, perform well for smooth functions but lose accuracy near discontinuities. This paper introduces a Selective Error-Correcting Adaptive Quadrature algorithm (SECAQ), a method designed to address this issue. SECAQ identifies intervals with large local error or sharp changes, estimates jump sizes using one-sided evaluations, and applies compact correction terms activated only near the discontinuity. These localized corrections restore smoothness within each subinterval and can enable the base quadrature rule to achieve its full theoretical accuracy. Numerical tests involving jumps, cusps, and oscillatory functions demonstrate that SECAQ restores fourth-order convergence for Simpson’s rule and achieves errors close to machine precision. Compared to the standard adaptive Simpson’s method, SECAQ reduces the number of function evaluations by up to 60% while maintaining low computational overhead. The method is particularly useful when discontinuity locations or jump sizes are known or can be reliably estimated

Author Biographies

Israa Essa Abed, Department of Networks and Computer Software, Al-Furat Al-Awsat Technical University, Babylon, Iraq

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Wafaa M. R. Shakir, Department of Networks and Computer Software, Al-Furat Al-Awsat Technical University, Babylon, Iraq

WAFAA MOHAMMED RIDHA SHAKIR (Member, IEEE) received the Ph.D. degree in communications and electronics engineering from the University of Technology, Baghdad, Iraq, in 2011. She has been a faculty member with the Technical Institute of Babylon, Al-Furat Al-Awsat Technical University, Babil, Iraq, since 2005. She was a Research Fellow with the Pennsylvania State University, University Park, PA, USA, and a Postdoctoral Fellow with The University of Queensland, Brisbane, QA, Australia. Since 2022, she has been an associate research fellow with Paris-Saclay University, France. She has been an associate professor of wireless communications engineering with the Department of Computer Networks and Software, Al-Furat Al-Awsat Technical University, since 2011. Her current research interests include artificial intelligence, modeling, design, and performance analysis of wireless communication systems.

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Published

20-Apr-2026

Issue

Vol. 39 No. 2 (2026)

Section

Mathematics

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This work is licensed under a Creative Commons Attribution 4.0 International License.

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How to Cite

[1]

Abed, I.E. and Shakir, W.M.R. 2026. Enhanced Numerical Techniques for Selective Integration Using Error Correction Methods. Ibn AL-Haitham Journal For Pure and Applied Sciences. 39, 2 (Apr. 2026), 242–254. DOI:https://doi.org/10.30526/39.2.4304.