Share This Article:

Behavior of the Numerical Integration Error

Abstract Full-Text HTML Download Download as PDF (Size:1196KB) PP. 1412-1426
DOI: 10.4236/am.2014.510133    4,532 Downloads   6,099 Views   Citations


In this work, we consider different numerical methods for the approximation of definite integrals. The three basic methods used here are the Midpoint, the Trapezoidal, and Simpson’s rules. We trace the behavior of the error when we refine the mesh and show that Richardson’s extrapolation improves the rate of convergence of the basic methods when the integrands are sufficiently differentiable many times. However, Richardson’s extrapolation does not work when we approximate improper integrals or even proper integrals from functions without smooth derivatives. In order to save computational resources, we construct an adaptive recursive procedure. We also show that there is a lower limit to the error during computations with floating point arithmetic.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Marinov, T. , Omojola, J. , Washington, Q. and Banks, L. (2014) Behavior of the Numerical Integration Error. Applied Mathematics, 5, 1412-1426. doi: 10.4236/am.2014.510133.


[1] Marinov, T.T. and Marinova, R.S. (2010) Coefficient Identification in Euler-Bernoulli Equation from Over-Posed Data. Journal of Computational and Applied Mathematics, 235, 450-459.
[2] Marinov, T.T. and Vatsala, A. (2008) Inverse Problem for Coefficient Identification in Euler-Bernoulli Equation. Computers and Mathematics with Applications, 56, 400-410.
[3] Ackleh, A.S., Kearfott, R.B. and Allen, E.J. (2009) Classical and Modern Numerical Analysis: Theory, Methods and Practice, Chapman & Hall/CRC Numerical Analysis and Scientific Computing. CRC Press, Boca Raton.
[4] Press, W.H. and Teukolsky, S.A. and Vetterling, W.T. and Flannery, B.P. (2007) Numerical Recipes: The Art of Scientific Computing. Cambridge University Press, New York.
[5] Forsythe, G.E. and Malcolm, M.A. and Moler, C.B. (1977) Computer Methods for Mathematical Computations. Prentice Hall Professional Technical Reference, Upper Saddle River.
[6] Marinov T.T. and Deng, K. (2011) Characteristic Line Based Schemes for Solving a Quasilinear Hierarchical Size-Structured Model. Journal of Scientific Computing, 46, 452-469.

comments powered by Disqus

Copyright © 2019 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.