Derivative-based trapezoid rule for the Riemann-Stieltjes integral
type: Item
instance of: scholarly article
title: Derivative-based trapezoid rule for the Riemann-Stieltjes integral
zbMATH Open document ID: 1407.65031
DOI: 10.1155/2014/874651
author: Weijing Zhao
author: Zhaoning Zhang
published in: Mathematical Problems in Engineering
publication date: 2019-02-08T00:00:00Z
review text: Summary: 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.
Mathematics Subject Classification ID: 65D30
Mathematics Subject Classification ID: 65P10
zbMATH DE Number: 7017502
Wikidata QID: Q59070339
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/874651
OpenAlex ID: W2012038069
cites work: Q4307619
cites work: Q4836494
cites work: Construction of concentration measures for general Lorenz curves using Riemann-Stieltjes integrals
cites work: Martingales and Stochastic Integrals
cites work: Q4340096
cites work: High-precision numerical integration: progress and challenges
cites work: Q3996272
cites work: Q5553606
cites work: Hadamard's inequality and trapezoid rules for the Riemann-Stieltjes integral
cites work: Relative convexity and quadrature rules for the Riemann-Stieltjes integral
cites work: Derivative-based closed Newton-Cotes numerical quadrature
cites work: Midpoint derivative-based closed Newton-Cotes quadrature
cites work: Newton--Cotes formulae for long-time integration.
cites work: New open modified Newton Cotes type formulae as multilayer symplectic integrators
cites work: Q3184863
cites work: Closed Newton-Cotes trigonometrically-fitted formulae of high order for the numerical integration of the Schrödinger equation
cites work: New open modified trigonometrically-fitted Newton-Cotes type multilayer symplectic integrators for the numerical solution of the Schrödinger equation
cites work: High order closed Newton-Cotes exponentially and trigonometrically fitted formulae as multilayer symplectic integrators and their application to the radial Schrödinger equation
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description: scientific article; zbMATH DE number 7017502