Derivative-Based Trapezoid Rule for the Riemann-Stieltjes Integral | Zendy

Weijing Zhao | Zendy; Zhaoning Zhang | Zendy

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Derivative-Based Trapezoid Rule for the Riemann-Stieltjes Integral

Author(s) -

Weijing Zhao,

Zhaoning Zhang

Publication year - 2014

Publication title -

mathematical problems in engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.262

H-Index - 62

eISSN - 1026-7077

pISSN - 1024-123X

DOI - 10.1155/2014/874651

Subject(s) - riemann–stieltjes integral , mathematics , derivative (finance) , generalization , riemann integral , riemann hypothesis , quadrature (astronomy) , mathematical analysis , integral equation , physics , singular integral , financial economics , optics , economics

The derivative-based trapezoid rule for the Riemann-Stieltjes integral is presented which uses 2 derivative values at the endpoints. This kind of quadrature rule obtains an increase of two orders of precision over the trapezoid rule for the Riemann-Stieltjes integral and the error term is investigated. At last, the rationality of the generalization of derivative-based trapezoid rule for Riemann-Stieltjes integral is demonstrated

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