A Proposed Numerical Integration Method Using Polynomial Interpolation

Darkwah, Kwasi A.; Nortey, Ezekiel N. N.; Lotsi, Charles Anani

doi:10.9734/bjmcs/2016/25299

Cited by 3 publications

(1 citation statement)

References 13 publications

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“…Furthermore, Marinov, T. et al used the three basic methods which are the Midpoint, the Trapezoidal, and Simpson's rules [21]. Kwasi A. et al proposed a numerical integration method using polynomial interpolation that provides improved estimates as compared to the Newton-Cotes methods of integration [22]. Also, Mir Md.…”

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

View full text Add to dashboard Cite

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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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