The second kind Chebyshev–Newton–Cotes quadrature rule (open type) and its numerical improvement

Hashemiparast, S. M.; Masjed‐Jamei, Mohammad; Eslahchi, M. R.; Dehghan, Mehdi

doi:10.1016/j.amc.2005.12.045

Cited by 4 publications

(2 citation statements)

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“…The concept of degree of precision was used to set a system of nonlinear equations to obtain the approximate values of the parameters involved by solving the system approximately. In 2006, these authors introduced improvements of first and second kind Chebyshev-Newton-Cotes quadrature rules [7,8]. In 2012, Burg introduced a new family of closed Newton-Cotes numerical integration formulas using first derivative values as well as functional values using the concept of degree of precision [9] to include additional parameters and thus to obtain new closed Newton-Cotes rules with increased order of accuracy.…”

Section: Introductionmentioning

confidence: 99%

New Derivative Based Open Newton-Cotes Quadrature Rules

Zafar

Saleem

Burg

2014

Abstract and Applied Analysis

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Some new families of open Newton-Cotes rules which involve the combinations of function values and the evaluation of derivative at uniformly spaced points of the interval are presented. The order of accuracy of these numerical formulas is higher than that of the classical open Newton-Cotes formulas. An extensive comparison of the computational cost, order of accuracy, error terms, coefficients of the error terms, observed order of accuracy, CPU usage time, and results obtained from these formulas is given. The comparisons show that we have been able to define some new open Newton-Cotes rules which are superior to classical open rules for less number of nodes and less computational cost with increased order of accuracy.

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Section: Introductionmentioning

confidence: 99%

New Derivative Based Open Newton-Cotes Quadrature Rules

Zafar

Saleem

Burg

2014

Abstract and Applied Analysis

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“…In recent years, many authors presented and improved different applicable algorithms about Newton-Cotes integration rules. Simos et al in [42,52,53,54,55], Burg in [19] and Sandu in [50] used this method for solving many applicable problems and Dehghan et al in [28,29], Hashemiparast et al in [38,39] and Eslahchi et al in [31] improved this method. The results of these works are obtained in the common computer arithmetic and the termination criterion usually depends on a positive and small real number like ε.…”

Section: Introductionmentioning

confidence: 99%

Finding optimal step of fuzzy Newton-Cotes integration rules by using the CESTAC method

Noeiaghdam¹,

Araghi²

2017

Journal of Fuzzy Set Valued Analysis

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The aim of this work, is to evaluate the value of a fuzzy integral by applying the Newton-Cotes integration rules via a reliable scheme. In order to perform the numerical examples, the CADNA (Control of Accuracy and Debugging for Numerical Applications) library and the CESTAC (Controle et Estimation Stochastique des Arrondis de Calculs) method are applied based on the stochastic arithmetic. By using this method, the optimal number of points in the fuzzy numerical integration rules and the optimal approximate solution are obtained. Also, the accuracy of the fuzzy quadrature rules are discussed. An algorithm is given to illustrate the implementation of the method. In this case, the termination criterion is considered as the Hausdorff distance between two sequential results to be an informatical zero. Two sample fuzzy integrals are evaluated based on the proposed algorithm to show the importance and advantage of using the stochastic arithmetic in place of the floating-point arithmetic.

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Open Newton - Cotes Quadrature With Midpoint Derivative for Integration of Algebraic Functions

Ramachandran¹

2015

IJRET

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The second kind Chebyshev–Newton–Cotes quadrature rule (open type) and its numerical improvement

Cited by 4 publications

References 4 publications

New Derivative Based Open Newton-Cotes Quadrature Rules

New Derivative Based Open Newton-Cotes Quadrature Rules

Finding optimal step of fuzzy Newton-Cotes integration rules by using the CESTAC method

Open Newton - Cotes Quadrature With Midpoint Derivative for Integration of Algebraic Functions

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