A Proposed Method for Numerical Integration

Mettle, Felix O.; Quaye, Enoch; Asiedu, Louis; Darkwah, Kwasi A.

doi:10.9734/bjmcs/2016/23048

Cited by 4 publications

(2 citation statements)

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“…Chapra SC showed in Applied Numerical Methods with MATLAB to learn and apply numerical methods to solve problems in engineering and science [18]. Mettle, F. O. propounded a numerical integration method that provides improved estimates as compared to the Newton-Cotes methods of integration [19]. Smyth, G. K. focused on the process of approximating a definite integral from values of the integrand when exact mathematical integration is not available [20].…”

Section: Introductionmentioning

confidence: 99%

A New Analysis of Approximate Solutions for Numerical Integration Problems with Quadrature-based Methods

Moheuddin¹,

Titu²,

Hossain³

2020

PAMJ

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In this paper, we mainly propose the approximate solutions to solve the integration problems numerically using the quadrature method including the Trapezoidal method, Simpson's 1/3 method, and Simpson's 3/8 method. The three proposed methods are quite workable and practically well suitable for solving integration problems. Through the MATLAB program, our numerical solutions are determined as well as compared with the exact values to verify the higher accuracy of the proposed methods. Some numerical examples have been utilized to give the accuracy rate and simple implementation of our methods. In this study, we have compared the performance of our solutions and the computational attempt of our proposed methods. Moreover, we explore and calculate the errors of the three proposed methods for the sake of showing our approximate solution's superiority. Then, among these three methods, we analyzed the approximate errors to prove which method shows more appropriate results. We also demonstrated the approximate results and observed errors to give clear idea graphically. Therefore, from the analysis, we can point out that only the minimum error is in Simpson's 1/3 method which will beneficial for the readers to understand the effectiveness in solving the several numerical integration problems.

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Section: Introductionmentioning

confidence: 99%

A New Analysis of Approximate Solutions for Numerical Integration Problems with Quadrature-based Methods

Moheuddin¹,

Titu²,

Hossain³

2020

PAMJ

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“…A method of extending the trapezoidal rule is proposed in [6] which takes the approximation of each segment one step further by subdividing the top part into rectangles, squares, and triangles. This allows for more accurate calculations of the area of each segment, as the sum of these geometric shapes plus the area of the lower part of the segment is added together.…”

Section: Introductionmentioning

confidence: 99%

Improved Mid-Point Derivative based Closed Newton-Cotes Quadrature Rule

Saand,

Rind,

Ahmed

et al. 2022

VFAST trans. math.

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The main motivation for this work lies in the construction of new and efficient methods to improve the efficiency index of ‘Mid-Point Derivative Based Closed Newton-Cotes Quadrature Rules’. Proposed methods use the derivative values at the mid-points in each strip of integrations such as Mid-Point Derivative Based Closed Trapezoidal, Simpson One Third, Simpson Three eight and Bool’s Rule. The degree of precision and order of accuracy of proposed methods are higher than all the existing methods. Furthermore, error terms of the proposed methods are calculated by using the concept of precision. An extensive comparison of the proposed formulas, classical and mid-point quadrature rules for the number of function evaluation, error terms, coefficient of error terms and results obtained from some different problems are given. The comparisons illustrate that the new proposed Closed Newton-Cotes Rules are much superior to Classical Rules and Zhao and Li’s ‘Mid-Point Derivative Based Closed Newton-Cotes Quadrature’ schemes.

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Estimation of the Gini coefficient for the lognormal distribution of income using the Lorenz curve

2016

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The main objective of the study is to compare the Newton–Cotes methods such as the Trapezium rule, Simpson 1/3 rule and Simpson 3/8 rule to estimate the area under the Lorenz curve and Gini coefficient of income using polynomial function with degree 5. Comparing the Gini coefficients of income computed from the Polynomial function with degree 5 for the Trapezium, Simpson 1/3 and Simpson 3/8 methods using the relative errors showed that the trapezium rule, Simpson’s 1/3 rule and Simpson’s 3/8 rule show negative biases with the Simpson 1/3 rule yielding the lowest absolute relative true error of 4.230711 %.

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A Proposed Method for Numerical Integration

Cited by 4 publications

References 0 publications

A New Analysis of Approximate Solutions for Numerical Integration Problems with Quadrature-based Methods

A New Analysis of Approximate Solutions for Numerical Integration Problems with Quadrature-based Methods

Improved Mid-Point Derivative based Closed Newton-Cotes Quadrature Rule

Estimation of the Gini coefficient for the lognormal distribution of income using the Lorenz curve

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