Kamran Malik ,Muhammad Mujtaba Shaikh,Kashif Memon,Muhammad Saleem Chandio,Abdul Wasim Shaikh,



Cubature,Double integrals,Heronian mean Derivative-based scheme,Precision,Order of accuracyLocal and global errors,Local and global errors,Trapezoid,


This study focuses on the Heronian mean derivative-based numerical cubature scheme to better evaluate double integrals' infinite limits. The proposed modifications rely on the Trapezoidal-type quadrature and cubature schemes. The aforementioned proposed scheme is important to numerically evaluate the complex double integrals, where the exact value is not available but the approximate values can only be obtained. With regards to higher precision and order of accuracy, the proposed Heronian derivative-based double integral scheme provides efficient results. The discussed scheme, in basic and composite forms, with local and global error terms is presented with necessary proofs with their performance evaluation against conventional Trapezoid rule through some numerical experiments. The consequently observed error distributions of the aforementioned scheme are found to be lower than the conventional Trapezoidal cubature scheme in composite form


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