Numerical Integration Schemes for Unequal Data Spacing
American Journal of Applied Mathematics
Volume 5, Issue 2, April 2017, Pages: 48-56
Received: Apr. 4, 2017; Accepted: Apr. 20, 2017; Published: Jun. 3, 2017
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Authors
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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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.
Keywords
Numerical Integration, Divided Difference, Quadrature, Monte-Carlo Integration
To cite this article
Md. Mamun-Ur-Rashid Khan, M. R. Hossain, Selina Parvin, Numerical Integration Schemes for Unequal Data Spacing, American Journal of Applied Mathematics. Vol. 5, No. 2, 2017, pp. 48-56. doi: 10.11648/j.ajam.20170502.12
Copyright
Copyright © 2017 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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