Numerical Integration Schemes for Unequal Data Spacing

Md. Mamun-Ur-Rashid Khan; M. R. Hossain; Selina Parvin

doi:doi:10.11648/j.ajam.20170502.12

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Numerical Integration Schemes for Unequal Data Spacing

Md. Mamun-Ur-Rashid Khan, M. R. Hossain, Selina Parvin

Published in American Journal of Applied Mathematics (Volume 5, Issue 2)

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), 2024. 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.

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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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TY  - JOUR
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
PY  - 2017
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
SP  - 48
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

Md. Mamun-Ur-Rashid Khan

Department of Mathematics, University of Dhaka, Dhaka, Bangladesh
M. R. Hossain

Department of Applied Mathematics, University of Dhaka, Dhaka, Bangladesh
Selina Parvin

Department of Mathematics, University of Dhaka, Dhaka, Bangladesh

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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

Copy | Download

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

Copy | Download

@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}
}

Copy | Download

TY  - JOUR
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
PY  - 2017
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
SP  - 48
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  -

Copy | Download