Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Published in:
Introduction to Scientific Computing Read chapter Read first chapter

2016 | OriginalPaper | Chapter

6. Numerical Integration

Author : Mark H. Holmes

Published in: Introduction to Scientific Computing and Data Analysis

Publisher: Springer International Publishing

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

The objective of this chapter is to derive and then test methods that can be used to evaluate the definite integral In most calculus textbooks the examples and problems dedicated to integration are not particularly complicated, although some require a clever combination of methods to carry out the integration. In the real world the situation is much worse. As an example, to find the deformation of an elastic body when compressed by a rigid punch it is necessary to evaluate (Gladwell [1980] Moreover, it is relatively easy to find integrals even worse than the one above. To illustrate, in the study of the emissions from a pulsar it is necessary to evaluate (Gwinn et al. [2012] where K 2 is the modified Bessel function. The point here is that effective numerical methods for evaluating integrals are needed, and our objective is to determine what they are.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

inform now
previous chapter Interpolation
next chapter Initial Value Problems
Literature
Gander, W., Gautschi, W.: Adaptive quadrature—revisited. BIT 40 (1), 84–101 (2000). ISSN 0006-3835. doi:10.1023/A:1022318402393
Gladwell, G.M.L.: Contact Problems in the Classical Theory of Elasticity. Sijthoff and Noordhoff, Germantown, MD (1980)CrossRefMATH
Golub, G.H., Welsch, J.H.: Calculation of Gauss quadrature rules. Math. Comput. 23 (106), 221–230 (1969). doi:10.3934/jcd.2014.1.391MathSciNetCrossRefMATH
Gonnet, P.: A review of error estimation in adaptive quadrature. ACM Comput. Surv. 44 (4), 22:1–22:36 (2012). ISSN 0360-0300. doi:10.1145/ 2333112.2333117
Gwinn, C.R., Johnson, M.D., Reynolds, J.E., Jauncey, D.L., Tzioumis, A.K., Dougherty, S., Carlson, B., Del Rizzo, D., Hirabayashi, H., Kobayashi, H., Murata, Y., Edwards, P.G., Quick, J.F.H., Flanagan, C.S., McCulloch, P.M.: Noise in the cross-power spectrum of the Vela pulsar. Astrophys. J. 758 (1), 6 (2012)CrossRef
Holmes, M.H.: Connections between cubic splines and quadrature rules. Am. Math. Mon. 121 (7), 661–662 (2014)MathSciNetMATH
Iserles, A., Nørsett, S.P., Olver, S.: Highly oscillatory quadrature: the story so far. In: de Castro, A.B., Gomez, D., Quintela, P., Salgado, P. (eds.) Numerical Mathematics and Advanced Applications, pp. 97–118. Springer, Berlin (2006). ISBN 978-3-540-34287-8. doi:10.1007/978-3-540-34288-5_6
Love, C.H.: Abscissas and Weights for Gaussian Quadrature for n=2 to 100, and n=125, 150, 175, and 200. National Bureau of Standards, U.S. Government Printing Office, Washington, DC (1966)MATH
Nenad, U., Roberts, A.J.: A corrected quadrature formula and applications. ANZIAM J. 45, E41–E56 (2008)MathSciNetMATH
Olver, F.W.J., Lozier, D.W., Boisvert, R.F., Clark, C.W.: NIST Handbook of Mathematical Functions. Cambridge University Press, Cambridge (2010)MATH
Trefethen, L.N., Weideman, J.A.C.: The exponentially convergent trapezoidal rule. SIAM Rev. 56 (3), 385–458 (2014). doi:10.1137/130932132MathSciNetCrossRefMATH
Waldvogel, J.: Towards a general error theory of the trapezoidal rule. In: Gautschi, W., Mastroianni, G., Rassias, T.M. (eds.) Approximation and Computation. Springer Optimization and Its Applications, vol. 42, pp. 267–282. Springer, New York (2011)
Metadata
Title
Numerical Integration
Author
Mark H. Holmes
Copyright Year
2016
Book
Introduction to Scientific Computing and Data Analysis

Print ISBN: 978-3-319-30254-6

Electronic ISBN: 978-3-319-30256-0

Copyright Year: 2016

DOI
https://doi.org/10.1007/978-3-319-30256-0_6

Premium Partner

    Image Credits