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Numerical Integration Schemes for Unequal Data Spacing

Received: 4 April 2017     Accepted: 20 April 2017     Published: 3 June 2017
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Abstract

In this Paper, we have derived the numerical integration formula for unequal data spacing. For doing so we use Newton’s Divided difference formula to evaluate general quadrature formula and then generate Trapezoidal and Simpson’s rules for the unequal data spacing with error terms. Finally we use numerical examples to compare the numerical results with analytical results and the well-known Monte- Carlo integration results and find excellent agreement.

Published in American Journal of Applied Mathematics (Volume 5, Issue 2)
DOI 10.11648/j.ajam.20170502.12
Page(s) 48-56
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), 2017. Published by Science Publishing Group

Keywords

Numerical Integration, Divided Difference, Quadrature, Monte-Carlo Integration

References
[1] Atkinson, K. E., 1978, An Introduction to Numerical Analysis, John Wiley & Sons, New York.
[2] Conte, S. D., 1965, Elementary Numerical Analysis, McGraw Hill, New York.
[3] Douglas Fairs, J., & L. Richard Burden, 2001, Numerical Analysis, Thomson Learning.
[4] Sastry, S. S., 2005, Introductory Methods of Numerical Analysis, Prentice-Hall of India.
[5] Ridgway Scott, L., 2011, Numerical Analysis, Princeton University press.
[6] Curtis F. Gerald, Patrick O. Wheatley, 2004, Applied Numerical Analysis, Pearson Education, Inc.
[7] William E. Boyce, Richard C. Diprima, 2001, Elementary Differential Equations and Boundary Value Problems, John Willey & Sons. Inc.
[8] Ward Cheney, David Kincaid, 2008, Numerical Mathematics and Computing, Thomson Brooks/Cole.
[9] F. B. Hildebrand, 1974, Introduction to Numerical Analysis, McGraw-Hill Book Company Inc.
[10] Alfio Quarteroni, Riccardo Sacco, Fausto Saleri, 2000, Numerical Mathematics, Springer-Verlag New York, Inc.
Cite This Article
  • APA Style

    Md. Mamun-Ur-Rashid Khan, M. R. Hossain, Selina Parvin. (2017). Numerical Integration Schemes for Unequal Data Spacing. American Journal of Applied Mathematics, 5(2), 48-56. https://doi.org/10.11648/j.ajam.20170502.12

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    ACS Style

    Md. Mamun-Ur-Rashid Khan; M. R. Hossain; Selina Parvin. Numerical Integration Schemes for Unequal Data Spacing. Am. J. Appl. Math. 2017, 5(2), 48-56. doi: 10.11648/j.ajam.20170502.12

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    AMA Style

    Md. Mamun-Ur-Rashid Khan, M. R. Hossain, Selina Parvin. Numerical Integration Schemes for Unequal Data Spacing. Am J Appl Math. 2017;5(2):48-56. doi: 10.11648/j.ajam.20170502.12

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  • @article{10.11648/j.ajam.20170502.12,
      author = {Md. Mamun-Ur-Rashid Khan and M. R. Hossain and Selina Parvin},
      title = {Numerical Integration Schemes for Unequal Data Spacing},
      journal = {American Journal of Applied Mathematics},
      volume = {5},
      number = {2},
      pages = {48-56},
      doi = {10.11648/j.ajam.20170502.12},
      url = {https://doi.org/10.11648/j.ajam.20170502.12},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20170502.12},
      abstract = {In this Paper, we have derived the numerical integration formula for unequal data spacing. For doing so we use Newton’s Divided difference formula to evaluate general quadrature formula and then generate Trapezoidal and Simpson’s rules for the unequal data spacing with error terms. Finally we use numerical examples to compare the numerical results with analytical results and the well-known Monte- Carlo integration results and find excellent agreement.},
     year = {2017}
    }
    

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    T1  - Numerical Integration Schemes for Unequal Data Spacing
    AU  - Md. Mamun-Ur-Rashid Khan
    AU  - M. R. Hossain
    AU  - Selina Parvin
    Y1  - 2017/06/03
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    N1  - https://doi.org/10.11648/j.ajam.20170502.12
    DO  - 10.11648/j.ajam.20170502.12
    T2  - American Journal of Applied Mathematics
    JF  - American Journal of Applied Mathematics
    JO  - American Journal of Applied Mathematics
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    EP  - 56
    PB  - Science Publishing Group
    SN  - 2330-006X
    UR  - https://doi.org/10.11648/j.ajam.20170502.12
    AB  - In this Paper, we have derived the numerical integration formula for unequal data spacing. For doing so we use Newton’s Divided difference formula to evaluate general quadrature formula and then generate Trapezoidal and Simpson’s rules for the unequal data spacing with error terms. Finally we use numerical examples to compare the numerical results with analytical results and the well-known Monte- Carlo integration results and find excellent agreement.
    VL  - 5
    IS  - 2
    ER  - 

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Author Information
  • Department of Mathematics, University of Dhaka, Dhaka, Bangladesh

  • Department of Applied Mathematics, University of Dhaka, Dhaka, Bangladesh

  • Department of Mathematics, University of Dhaka, Dhaka, Bangladesh

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