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 |
Numerical Integration, Divided Difference, Quadrature, Monte-Carlo Integration
| [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. |
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
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
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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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}
}
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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