# SOME NEW AND EFFICIENT DERIVATIVE-BASED SCHEMES FOR NUMERICAL CUBATURE

#### DOI NO:

https://doi.org/10.26782/jmcms.2020.10.00005

#### Keywords:

Cubature,Double integrals,Derivative-based schemes,Precision,Order of accuracy,Trapezoid,

#### Abstract

In this research work, some new derivative-based numerical cubature schemes have been proposed for the accurate evaluation of double integrals under finite range. The proposed modifications are based on the Trapezoidal-type quadrature and cubature rules. The proposed schemes are important to numerically evaluate the complex double integrals, where the exact value is not available but the approximate values can only be obtained. The proposed derivative-based double integral schemes provide efficient results with regards to higher precision and order of accuracy. The proposed schemes, in basic and composite forms, with local and global error terms are presented with necessary proofs with their performance evaluation against conventional Trapezoid rule through some numerical experiments. The consequent observed error distributions of the proposed schemes are found to be lower than the conventional Trapezoidal cubature scheme in composite form

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