Contra-Harmonic Mean Derivative-Based Open Newton-Cotes Quadrature Rules
DOI:
https://doi.org/10.26692/surjss.v57i02.7752Keywords:
Quadrature rule, Contra-Harmonic Mean, Open Newton-Cotes, Error Terms, Local Error, Global ErrorAbstract
A novel family of open Newton-Cotes formulas is created to assess definite integrals. The new family is formed by taking the Contra-Harmonic Mean of the function's first-order derivatives within the interval [a,b]. In comparison to the classical open Newton-Cotes quadrature rules, the proposed derivative-based quadrature rules improve accuracy by two orders of magnitude. These formulas arise from the concept of degree of precision. Furthermore, the theoretical conclusions are validated by calculating the computational order of accuracy for each approach. The computational cost and absolute error drops calculated for three different integrals from the literature illustrate the superiority of the proposed approaches over the classical method.
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