Authors:
Kamran Malik ,Muhammad Mujtaba Shaikh,Muhammad Saleem Chandio,Abdul Wasim Shaikh,DOI NO:
https://doi.org/10.26782/jmcms.2020.11.00009Keywords:
Cubature,Double integrals,closed Newton-Cotes,Precision,Order of accuracy,Local error,Computational cost,Abstract
Numerical integration is one of the fundamental tools of numerical analysis to cope with the complex integrals which cannot be evaluated analytically, and for the cases where the integrand is not mathematically known in closed form. The quadrature rules are used for approximating single integrals, whereas cubature rules are used to evaluate integrals in higher dimensions. In this work, we consider the closed Newton-Cotes cubature schemes for double integrals and discuss consequent error analysis of these schemes in terms of the degree of precision, local error terms for the basic form approximations, composite forms and the global error terms. Besides, the computational cost of the implementation of these schemes is also presented. The theorems proved in this work area pioneering investigation on error analysis of such schemes in the literature.Refference:
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