Full Text Available
Note: Clicking the button above will open the full text document at the original institutional repository in a new window.
Foutanalisemetodes vir numeriese integrasiereels op ekwidistante partisies
Tesis (M. Sc.) -- Universiteit van Stellenbosch, 1990.
Saved in:
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Thesis |
| Language: | Afrikaans |
| Published: |
Stellenbosch : Stellenbosch University
2012
|
| Subjects: | |
| Tags: |
No Tags, Be the first to tag this record!
|
| _version_ | 1867613811297484800 |
|---|---|
| access_status_str | Open Access |
| author | De Swardt, Susan |
| author2 | De Villiers, J. M. |
| author_browse | De Swardt, Susan De Villiers, J. M. |
| author_facet | De Villiers, J. M. De Swardt, Susan |
| author_sort | De Swardt, Susan |
| collection | Thesis |
| dc_rights_str_mv | Stellenbosch University |
| description | Tesis (M. Sc.) -- Universiteit van Stellenbosch, 1990. |
| format | Thesis |
| id | oai:scholar.sun.ac.za:10019.1/68823 |
| institution | Stellenbosch University (South Africa) |
| language | Afrikaans |
| last_indexed | 2026-06-10T12:42:04.592Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from SUNScholar — Stellenbosch University Repository |
| publishDate | 2012 |
| publishDateRange | 2012 |
| publishDateSort | 2012 |
| publisher | Stellenbosch : Stellenbosch University |
| publisherStr | Stellenbosch : Stellenbosch University |
| record_format | dspace |
| source_str | SUNScholar — Stellenbosch University Repository |
| spelling | oai:scholar.sun.ac.za:10019.1/68823 Foutanalisemetodes vir numeriese integrasiereels op ekwidistante partisies De Swardt, Susan De Villiers, J. M. Stellenbosch University. Faculty of Science. Dept. of Applied Mathematics. Numerical integration Error analysis (Mathematics) Interpolation Dissertations -- Applied mathematics Tesis (M. Sc.) -- Universiteit van Stellenbosch, 1990. In this thesis various numerical integration techniques for the approximation of definite integrals are constructed and then compared by means of an analysis of their respective error expressions. Special emphasis is placed on the Newton-Cotes quadrature formules based on an equidistant partition of the integration interval. Our basic approach is to increase the accuracy of the trapezoidal rule in two different ways; firstly, by means of quadratic and higher order polynomial interpolation, and secondly by applying the method of endpoint corrections as deducted from the Euler-Maclaurin formula. For the latter formula we give here, in addition to a standard method of proof, an alternative proof based on finite Taylor series which has the further useful byproduct of a new representation formula for the even order Bernoulli polynomials. The application of endpoint corrections to the trapezoidal rule then leads to the construction of the Euler-Maclaurin quadrature formula and the Gregory rule. The theoretically predicted convergence orders of the various quadrature formulas are illustrated throughout the thesis by means of numerical examples. Masters 2012-08-27T12:26:47Z 2012-08-27T12:26:47Z 1990 Thesis http://hdl.handle.net/10019.1/68823 af Stellenbosch University 113 pages : ill. application/pdf Stellenbosch : Stellenbosch University |
| spellingShingle | Numerical integration Error analysis (Mathematics) Interpolation Dissertations -- Applied mathematics De Swardt, Susan Foutanalisemetodes vir numeriese integrasiereels op ekwidistante partisies |
| title | Foutanalisemetodes vir numeriese integrasiereels op ekwidistante partisies |
| title_full | Foutanalisemetodes vir numeriese integrasiereels op ekwidistante partisies |
| title_fullStr | Foutanalisemetodes vir numeriese integrasiereels op ekwidistante partisies |
| title_full_unstemmed | Foutanalisemetodes vir numeriese integrasiereels op ekwidistante partisies |
| title_short | Foutanalisemetodes vir numeriese integrasiereels op ekwidistante partisies |
| title_sort | foutanalisemetodes vir numeriese integrasiereels op ekwidistante partisies |
| topic | Numerical integration Error analysis (Mathematics) Interpolation Dissertations -- Applied mathematics |
| url | http://hdl.handle.net/10019.1/68823 |
| work_keys_str_mv | AT deswardtsusan foutanalisemetodesvirnumerieseintegrasiereelsopekwidistantepartisies |