Comparison of Arithmetic Mean, Geometric Mean and Harmonic Mean Derivative-Based Closed Newton Cotes Quadrature
نویسنده
چکیده
In this paper, the computation of numerical integration using arithmetic mean (AMDCNC), geometric mean (GMDCNC) and harmonic mean (HMDCNC) derivativebased closed Newton cotes quadrature rules are compared with the existing closed Newton cotes quadrature rule (CNC). The comparison shows that, arithmetic mean-based rule gives better solution than the other two rules. This set of quadrature rules which includes the mean value at the function derivative for the computation of numerical integration and the error terms are also obtained by using the concept of precision. Finally, the mathematical relationship between the rules AM > GM > HM are analyzed using numerical examples and the results are compared with the existing methods. Keyword: Numerical integration, Closed Newton-cotes formula, Arithmetic mean derivative, Geometric mean derivative, Harmonic mean derivative, Numerical examples. AMS Mathematics Subject Classification (2010): 65D30, 65D32
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