Skip to main content

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
Cancel
×
×
Home
  • Home
Article
  • Access

GENERAL THREE-POINT QUADRATURE FORMULAS OF EULER TYPE

  • IVA FRANJIĆ (a1), JOSIP PEČARIĆ (a2) and IVAN PERIĆ (a1)
Abstract

General three-point quadrature formulas for the approximate evaluation of an integral of a function f over [0,1], through the values f(x), f(1/2), f(1−x), f′(0) and f′(1), are derived via the extended Euler formula. Such quadratures are sometimes called “corrected” or “quadratures with end corrections” and have a higher accuracy than the adjoint classical formulas, which only include the values f(x), f(1/2) and f(1−x) . The Gauss three-point, corrected Simpson, corrected dual Simpson, corrected Maclaurin and corrected Gauss two-point formulas are recaptured as special cases. Finally, sharp estimates of error are given for this type of quadrature formula.

    •
      • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      GENERAL THREE-POINT QUADRATURE FORMULAS OF EULER TYPE
      Available formats
      ×
      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      GENERAL THREE-POINT QUADRATURE FORMULAS OF EULER TYPE
      Available formats
      ×
      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      GENERAL THREE-POINT QUADRATURE FORMULAS OF EULER TYPE
      Available formats
      ×
Copyright
COPYRIGHT: © Australian Mathematical Society 2011
Corresponding author
✉For correspondence; e-mail: ifranjic@pbf.hr
References
Hide All
[1]Abramowitz, M. and Stegun (eds), I. A., Handbook of mathematical functions: with formulas, graphs and mathematical tables (Dover Publications, New York, 1992).
[2]Dedić, Lj., Matić, M. and Pečarić, J., “On generalizations of Ostrowski inequality via some Euler-type identities”, Math. Inequal. Appl. 3 (2000) 337–353.
[3]Franjić, I. and Pečarić, J., “Corrected Euler–Maclaurin’s formulae”, Rend. Circ. Mat. Palermo 54 (2005) 259–272; doi:10.1007/BF02874640.
[4]Franjić, I. and Pečarić, J., “On corrected dual Euler–Simpson formulae”, Soochow J. Math. 32 (2006) 575–587.
[5]Franjić, I., Perić, I. and Pečarić, J., “Quadrature formulae of Gauss type based on Euler identities”, Math. Comput. Modelling 45 (2007) 355–370; doi:10.1016/j.mcm.2006.05.009.
[6]Hildebrand, F. B., Introduction to numerical analysis (McGraw-Hill, New York, 1956).
[7]Krylov, V. I., Approximate calculation of integrals (Macmillan, New York–London, 1962).
[8]Lanczos, C., Applied analysis (Prentice-Hall, Englewood Cliffs, NJ, 1956).
[9]Pečarić, J. and Franjić, I., “Generalisation of a corrected Simpson’s formula”, ANZIAM J. 47 (2006) 367–385; doi:10.1017/S1446181100009895.
[10]Pečarić, J., Perić, I. and Vukelić, A., “Sharp integral inequalities based on general Euler two-point formulae”, ANZIAM J. 46 (2005) 555–574; doi:10.1017/S1446181100009676.
[11]Ujević, N. and Roberts, A. J., “A corrected quadrature formula and applications”, ANZIAM J. 45(E) (2004) E41–E56.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

The ANZIAM Journal
  • ISSN: 1446-1811
  • EISSN: 1446-8735
  • URL: /core/journals/anziam-journal
Please enter your name
Please enter a valid email address
Who would you like to send this to? *

CAPTCHA *

Skip to the audio challenge
×
MathJax

Keywords:

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 31 *
Loading metrics...

Abstract views

Total abstract views: 80 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 12th June 2018. This data will be updated every 24 hours.

Cancel
Confirm
×