Open AccessMidpoint Derivative-Based Closed Newton-Cotes Quadrature
Author(s) -
Weijing Zhao,
Hongxing Li
Publication year - 2013
Publication title -
abstract and applied analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.228
H-Index - 56
eISSN - 1687-0409
pISSN - 1085-3375
DOI - 10.1155/2013/492507
Subject(s) - mathematics , midpoint , numerical integration , quadrature (astronomy) , gauss–jacobi quadrature , gauss–kronrod quadrature formula , midpoint method , newton's method , numerical analysis , mathematical analysis , tanh sinh quadrature , clenshaw–curtis quadrature , gaussian quadrature , geometry , nyström method , nonlinear system , boundary value problem , physics , electrical engineering , quantum mechanics , engineering
A novel family of numerical integration of closed Newton-Cotes quadrature rules is presented which uses the derivative value at the midpoint. It is proved that these kinds of quadrature rules obtain an increase of two orders of precision over the classical closed Newton-Cotes formula, and the error terms are given. The computational cost for these methods is analyzed from the numerical point of view, and it has shown that the proposed formulas are superior computationally to the same order closed Newton-Cotes formula when they reduce the error below the same level. Finally, some numerical examples show the numerical superiority of the proposed approach with respect to closed Newton-Cotes formulas
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