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

Mir Md. Moheuddin; Muhammad Abdus Sattar Titu; Saddam Hossain

doi:doi:10.11648/j.pamj.20200903.11

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

Mir Md. Moheuddin, Muhammad Abdus Sattar Titu, Saddam Hossain

Published in Pure and Applied Mathematics Journal (Volume 9, Issue 3)

Received: 4 May 2020 Accepted: 9 June 2020 Published: 20 June 2020

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Abstract

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.

Published in	Pure and Applied Mathematics Journal (Volume 9, Issue 3)
DOI	10.11648/j.pamj.20200903.11
Page(s)	46-54
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2020. Published by Science Publishing Group

Keywords

Numerical Integration, Trapezoidal Method, Simpson’s One-Third Method, Simpson’s Three-eighth’s Method

References

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APA Style

Mir Md. Moheuddin, Muhammad Abdus Sattar Titu, Saddam Hossain. (2020). A New Analysis of Approximate Solutions for Numerical Integration Problems with Quadrature-based Methods. Pure and Applied Mathematics Journal, 9(3), 46-54. https://doi.org/10.11648/j.pamj.20200903.11

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ACS Style

Mir Md. Moheuddin; Muhammad Abdus Sattar Titu; Saddam Hossain. A New Analysis of Approximate Solutions for Numerical Integration Problems with Quadrature-based Methods. Pure Appl. Math. J. 2020, 9(3), 46-54. doi: 10.11648/j.pamj.20200903.11

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AMA Style

Mir Md. Moheuddin, Muhammad Abdus Sattar Titu, Saddam Hossain. A New Analysis of Approximate Solutions for Numerical Integration Problems with Quadrature-based Methods. Pure Appl Math J. 2020;9(3):46-54. doi: 10.11648/j.pamj.20200903.11

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@article{10.11648/j.pamj.20200903.11,
  author = {Mir Md. Moheuddin and Muhammad Abdus Sattar Titu and Saddam Hossain},
  title = {A New Analysis of Approximate Solutions for Numerical Integration Problems with Quadrature-based Methods},
  journal = {Pure and Applied Mathematics Journal},
  volume = {9},
  number = {3},
  pages = {46-54},
  doi = {10.11648/j.pamj.20200903.11},
  url = {https://doi.org/10.11648/j.pamj.20200903.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20200903.11},
  abstract = {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.},
 year = {2020}
}

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TY - JOUR
T1 - A New Analysis of Approximate Solutions for Numerical Integration Problems with Quadrature-based Methods
AU - Mir Md. Moheuddin
AU - Muhammad Abdus Sattar Titu
AU - Saddam Hossain
Y1 - 2020/06/20
PY - 2020
N1 - https://doi.org/10.11648/j.pamj.20200903.11
DO - 10.11648/j.pamj.20200903.11
T2 - Pure and Applied Mathematics Journal
JF - Pure and Applied Mathematics Journal
JO - Pure and Applied Mathematics Journal
SP - 46
EP - 54
PB - Science Publishing Group
SN - 2326-9812
UR - https://doi.org/10.11648/j.pamj.20200903.11
AB - 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.
VL - 9
IS - 3
ER -

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Author Information

Mir Md. Moheuddin

Department of CSE (Mathematics), Atish Dipankar University of Science and Technology (ADUST), Dhaka, Bangladesh
Muhammad Abdus Sattar Titu

Department of Mathematics (General Science), Mymensingh Engineering College (MEC), Mymensingh, Bangladesh
Saddam Hossain

Department of Basic Science (Mathematics), World University of Bangladesh (WUB), Dhaka, Bangladesh

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APA Style

Mir Md. Moheuddin, Muhammad Abdus Sattar Titu, Saddam Hossain. (2020). A New Analysis of Approximate Solutions for Numerical Integration Problems with Quadrature-based Methods. Pure and Applied Mathematics Journal, 9(3), 46-54. https://doi.org/10.11648/j.pamj.20200903.11

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ACS Style

Mir Md. Moheuddin; Muhammad Abdus Sattar Titu; Saddam Hossain. A New Analysis of Approximate Solutions for Numerical Integration Problems with Quadrature-based Methods. Pure Appl. Math. J. 2020, 9(3), 46-54. doi: 10.11648/j.pamj.20200903.11

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AMA Style

Mir Md. Moheuddin, Muhammad Abdus Sattar Titu, Saddam Hossain. A New Analysis of Approximate Solutions for Numerical Integration Problems with Quadrature-based Methods. Pure Appl Math J. 2020;9(3):46-54. doi: 10.11648/j.pamj.20200903.11

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@article{10.11648/j.pamj.20200903.11,
  author = {Mir Md. Moheuddin and Muhammad Abdus Sattar Titu and Saddam Hossain},
  title = {A New Analysis of Approximate Solutions for Numerical Integration Problems with Quadrature-based Methods},
  journal = {Pure and Applied Mathematics Journal},
  volume = {9},
  number = {3},
  pages = {46-54},
  doi = {10.11648/j.pamj.20200903.11},
  url = {https://doi.org/10.11648/j.pamj.20200903.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20200903.11},
  abstract = {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.},
 year = {2020}
}

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