New Derivative Based Open Newton-Cotes Quadrature Rules

Zafar, Fiza; Saleem, Saira; Burg, Clarence O. E.

doi:10.1155/2014/109138

Cited by 18 publications

(7 citation statements)

References 10 publications

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“…Due to the higher number of function evaluations at each integration step, a quadrature rule might provide reasonable accuracy in fewer steps but could also be computationally more expensive and less effective than other approaches. In the third part, the computational order of accuracy is calculated using the following formula, defined in [11].…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

Centroidal Mean Derivative-Based Open Newton-Cotes Quadrature Rules

Mahesar,

Shaikh,

Chandio

et al. 2023

VFAST trans. math.

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In this work, a new derivative-based family of open Newton-Cotes quadrature rules based on centroidal mean (CMDONC) is proposed for the estimation of definite integrals. The error terms of the modified methods are derived through the concept of precision. The local and global order of accuracy and precision for each method is also computed. The results show that the proposed methods achieve two orders of accuracy enhancement over the conventional Newton-Cotes quadrature rules (ONC). Lastly, two numerical tests are also observed which demonstrate the superiority of CMDONC rules over the classical ONC methods.

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Section: Numerical Results and Discussionmentioning

confidence: 99%

Centroidal Mean Derivative-Based Open Newton-Cotes Quadrature Rules

Mahesar,

Shaikh,

Chandio

et al. 2023

VFAST trans. math.

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“…The precision, the orders and the error terms for M ct [16] and proposed method M cta are shown in Table 2.…”

Section: Error Analysismentioning

confidence: 99%

Arithmetic mean derivative based midpoint rule

Marjulisa¹,

Imran²,

Syamsudhuha³

2018

ams

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In this article, we discuss the modification of double midpoint rule and corrected midpoint rule by adding the derivative evaluated at arithmetic mean of the nodes to approximate a definite integral. The proposed rules give increase of precision over the existing rules. Lastly, the effectiveness of the proposed rules is illustrated by numerical examples and the results are compared with the existing rules.

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“…for given n+1 distinct points x 0 < x 1 < ... < x n and n+1 weights w 0 , w 1 , ..., w n over the interval (a , b) with x i = a + ( i + 1) h, i = 0,1,2,...,n and ℎ = − +2 [ 7 ] .…”

Section: =0mentioning

confidence: 99%