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A close look at Newton–Cotes integration rules

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dc.contributor.author Sermutlu, Emre
dc.date.accessioned 2020-04-29T21:40:55Z
dc.date.available 2020-04-29T21:40:55Z
dc.date.issued 2019
dc.identifier.citation Sermutlu, Emre. "A close look at Newton–Cotes integration rules", Results in Nonlinear Analysis, Vol. 2, No. 2, pp. 48-60, (2019). tr_TR
dc.identifier.issn 2636-7556
dc.identifier.uri http://hdl.handle.net/20.500.12416/3512
dc.description.abstract Newton–Cotes integration rules are the simplest methods in numerical integration. The main advantage of using these rules in quadrature software is ease of programming. In practice, only the lower orders are implemented or tested, because of the negative coefficients of higher orders. Most textbooks state it is not necessary to go beyond Boole’s 5-point rule. Explicit coefficients and error terms for higher orders are seldom given literature. Higher-order rules include negative coefficients therefore roundoff error increases while truncation error decreases as we increase the number of points. But is the optimal one really Simpson or Boole? In this paper, we list coefficients up to 19-points for both open and closed rules, derive the error terms using an elementary and intuitive method, and test the rules on a battery of functions to find the optimum all-round one. tr_TR
dc.language.iso eng tr_TR
dc.rights info:eu-repo/semantics/openAccess tr_TR
dc.subject Quadrature tr_TR
dc.subject Newton–Cotes tr_TR
dc.subject Truncation Error tr_TR
dc.subject MATLAB tr_TR
dc.title A close look at Newton–Cotes integration rules tr_TR
dc.type article tr_TR
dc.relation.journal Results in Nonlinear Analysis tr_TR
dc.contributor.authorID 17647 tr_TR
dc.identifier.volume 2 tr_TR
dc.identifier.issue 2 tr_TR
dc.identifier.startpage 48 tr_TR
dc.identifier.endpage 60 tr_TR
dc.contributor.department Çankaya Üniversitesi, Fen-Edebiyat Fakültesi, Matematik Bölümü tr_TR


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