A novel integral rule that uses the Nk1 rule to numerically compute the values of double integrals

Al-Karamy, Nada A. M.; Hilal, Rana Hasan; Mousa, Zainab Imran

doi:10.47974/JIM-2537

Open Access Research Article

A novel integral rule that uses the Nk1 rule to numerically compute the values of double integrals

^*Nada A. M. Al-KaramyCorresponding authornadaa.kharmi@uokufa.edu.iqDepartment of MathematicsFaculty of Education for WomenUniversity of KufaKufa, Najaf, 54001, Iraq0000-0003-4256-1562View full profile → , Rana Hasan Hilalranah.salman@uokufa.edu.iqDepartment of MathematicsFaculty of Education for WomenUniversity of KufaKufa, Najaf, 54001, Iraq0000-0001-7749-3008View full profile → , Zainab Imran MousaZainabu.ghrban@uokufa.edu.iqDepartment of MathematicsFaculty of Education for WomenUniversity of KufaKufa, Najaf, 54001, IraqView full profile →

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pp. 1487–1496Vol. 29Issue 5-BMay 2026DOI: 10.47974/JIM-2537XML

Received:: 01 Nov 2025
Published Online:: 27 Jun 2026
Article type:: Research Article
Language:: EN
Article no.:: JIM-2537
Pages:: 1487–1496

Abstract

The aims for the work are to derive a numerical method to find a value for the double integral, which is integrable either continuously or continuously, but its derivative is singular or singular at one or both ends, for an integration using the author rule to find the error formulas associated with it, improving the results using Romberg’s acceleration. It delivers high-accuracy results quickly, even with a few partial periods. and comparing a result for a new rule and a result for rule (SS, TT, MM, ST, SM, MT) of accuracy and speed of approach.

Keywords

Numerical integration Romperk accelerating Taylor series

Subject Classifications

Primary 93A30Secondary 49K15

References

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