Deriving a new complex rule for calculating double integrals using Boole’s Rule

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

doi:10.47974/JIM-2550

Open Access Research Article

Deriving a new complex rule for calculating double integrals using Boole’s Rule

^*Rana Hasan HilalCorresponding authorranah.salman@uokufa.edu.iqDepartment of MathematicsFaculty of Education for WomenUniversity of KufaKufa, Najaf, 54001, Iraq0000-0001-7749-3008View full profile → , Nada A. M. Al-Karamynadaa.kharmi@uokufa.edu.iqDepartment of MathematicsFaculty of Education for WomenUniversity of KufaKufa, Najaf, 54001, Iraq0000-0003-4256-1562View 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. 1573–1583Vol. 29Issue 5-BMay 2026DOI: 10.47974/JIM-2550XML

Received:: 01 Nov 2025
Published Online:: 27 Jun 2026
Article type:: Research Article
Language:: EN
Article no.:: JIM-2550
Pages:: 1573–1583

Abstract

The primary region. The first rule is composed of Boole’s rule for the inner dimension and the midpoint rule for the outer dimension. The second rule is composed of Boole’s rule on both internal dimensions. The goal of the research is to formulate two rules for determining the values of the continuous double integral inside the integration x, y, with the extraction of the correction limits that come with the two rules, and making use of them by extracting them, using the Romberg-Regardson acceleration, and comparing the accuracy and speed of approach to the exact value.

Keywords

Numerical integration Richardson extrapolation Taylor series Newton–cotes formulas

Subject Classifications

65D3065D3265B9930K05

References

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