Arithmetic mean derivative based midpoint rule

Marjulisa, Rike; Imran, Muhammad; Syamsudhuha,

doi:10.12988/ams.2018.8458

Cited by 4 publications

(4 citation statements)

References 8 publications

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“…In this section, various numerical tests have been taken on proposed quadrature rules, which confirm the validity of the theoretical results. Two numerical problems have been solved for each scheme taken from [27] and [28] respectively, which were determined using MATLAB (R2014b) Software. All the results are noted in Intel (R) Core i5 Laptop with RAM of 8.00 GB and a processing speed of 1.8 GHz.…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

“…The consequent observed error distributions are discovered to be smaller than the typical Trapezoidal cubature scheme in composite form. Two derivative-based schemes were introduced for closed Newton-Cotes rules in which the harmonic mean and contra-harmonic mean [27] were used. These schemes were proved to be more effective than the standard CNC formulas, in terms of error terms and approximate integral values.…”

Section: Introductionmentioning

confidence: 99%

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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%

Section: Introductionmentioning

confidence: 99%

Centroidal Mean Derivative-Based Open Newton-Cotes Quadrature Rules

Mahesar,

Shaikh,

Chandio

et al. 2023

VFAST trans. math.

View full text Add to dashboard Cite

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“…The accuracy of this rule is fifth Proof. Let that 𝑓(𝑥) in equation ( 4) is verified by 𝑓(𝑥) = Table 1 shows the precision, ordering, and error terms for the quartet midpoint rule (Mq) [6], double midpoint rule based on the arithmetic mean derivative (Mda) [4], midpoint rule based on the arithmetic mean derivative (Mm) [14], Simpson's are approximated 4 by Mq [6], Mda [4], S [11], M m [14], and Mqa. The results of this simulation were obtained using Octave software…”

Section: Error Analysismentioning

confidence: 99%

“…[15] enhanced the modified midpoint rule by determining a linear combination of both the function with the derivative of it values at the node points. Lately, we proposed double midpoint rule [4] and corrected closed Newton-Cotes [5] by adding arithmetic mean derivative in their endpoints.…”

Section: Introductionmentioning

confidence: 99%

Arithmetic Mean Derivative-Based Quartet Midpoint Rule

Marjulisa,

Putri

2023

Euler J. Ilm. Mat. Sains dan Teknol.

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A definite integral that is difficult to solve analytically can be calculated using the numerical integration methods. The midpoint rule is a prominent rule for approximating definite integrals. This article discusses a version of the quartet midpoint rule that includes the derivative of the arithmetic mean . The proposed rule increases precision over the previous rules. Furthermore, the error term is obtained by using the concept of precision between quadrature and exact values. Finally, the proposed rule is more effective than the present rule, according to numerical simulation results.

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