On families of quadrature formulas based on Euler identities
A family consisting of quadrature formulas which are exact for all polynomials of order ⩽5 is studied. Changing the coefficients, a second family of quadrature formulas, with the degree of exactness higher than that of the formulas from the first family, is produced. These formulas contain values of...
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| Published in | Applied mathematics and computation Vol. 217; no. 9; pp. 4516 - 4528 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Amsterdam
Elsevier Inc
2011
Elsevier |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0096-3003 1873-5649 |
| DOI | 10.1016/j.amc.2010.11.002 |
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| Abstract | A family consisting of quadrature formulas which are exact for all polynomials of order ⩽5 is studied. Changing the coefficients, a second family of quadrature formulas, with the degree of exactness higher than that of the formulas from the first family, is produced. These formulas contain values of the first derivative at the end points of the interval and are sometimes called “corrected”. |
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| AbstractList | A family consisting of quadrature formulas which are exact for all polynomials of order [inline image]5 is studied. Changing the coefficients, a second family of quadrature formulas, with the degree of exactness higher than that of the formulas from the first family, is produced. These formulas contain values of the first derivative at the end points of the interval and are sometimes called "corrected". A family consisting of quadrature formulas which are exact for all polynomials of order ⩽5 is studied. Changing the coefficients, a second family of quadrature formulas, with the degree of exactness higher than that of the formulas from the first family, is produced. These formulas contain values of the first derivative at the end points of the interval and are sometimes called “corrected”. |
| Author | Pečarić, Josip Perić, Ivan Franjić, Iva |
| Author_xml | – sequence: 1 givenname: Iva surname: FRANJIC fullname: FRANJIC, Iva organization: Faculty of Food Technology and Biotechnology, University of Zagreb, Pierottijeva 6, 10000 Zagreb, Croatia – sequence: 2 givenname: Josip surname: PECARIC fullname: PECARIC, Josip organization: Faculty of Textile Technology, University of Zagreb, Prilaz baruna Filipovića 30, 10000 Zagreb, Croatia – sequence: 3 givenname: Ivan surname: PERIC fullname: PERIC, Ivan organization: Faculty of Food Technology and Biotechnology, University of Zagreb, Pierottijeva 6, 10000 Zagreb, Croatia |
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| Keywords | Corrected quadrature formulas Extended Euler formulas Gauss formulas Bernoulli polynomials Closed 5-point quadrature formulas Sharp estimates of error Lobatto formulas Polynomial Numerical integration Error estimation Gauss formula Numerical analysis Applied mathematics Quadrature formula |
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| References | Lanczos (b0005) 1956 Dedić, Matić, Pečarić (b0015) 2000; 3 M. Abramowitz, I.A. Stegun (Eds.), Handbook of mathematical functions with formulas, graphs and mathematical tables, National Bureau of Standards, Appl. Math. Ser. 55, 4th printing, Washington, 1965. Krylov (b0025) 1962 Franjić, Pečarić, Perić (b0035) 2005; 8 Franjić, Pečarić, Perić (b0030) 2007; 45 Ujević, Roberts (b0010) 2004; 45 Franjić, Pečarić, Perić (b0040) 2009; 12 Ujević (10.1016/j.amc.2010.11.002_b0010) 2004; 45 Franjić (10.1016/j.amc.2010.11.002_b0040) 2009; 12 Dedić (10.1016/j.amc.2010.11.002_b0015) 2000; 3 Franjić (10.1016/j.amc.2010.11.002_b0030) 2007; 45 10.1016/j.amc.2010.11.002_b0020 Krylov (10.1016/j.amc.2010.11.002_b0025) 1962 Franjić (10.1016/j.amc.2010.11.002_b0035) 2005; 8 Lanczos (10.1016/j.amc.2010.11.002_b0005) 1956 |
| References_xml | – volume: 12 start-page: 573 year: 2009 end-page: 586 ident: b0040 article-title: General closed 4-point quadrature formulae of Euler type publication-title: Math. Inequal. Appl. – volume: 45 start-page: E41 year: 2004 end-page: E56 ident: b0010 article-title: A corrected quadrature formula and applications publication-title: ANZIAM J. – volume: 45 start-page: 355 year: 2007 end-page: 370 ident: b0030 article-title: Quadrature formulas of Gauss type based on Euler identities publication-title: Math. Comput. Modelling – volume: 3 start-page: 337 year: 2000 end-page: 353 ident: b0015 article-title: On generalizations of Ostrowski inequality via some Euler-type identities publication-title: Math. Inequal. Appl. – reference: M. Abramowitz, I.A. Stegun (Eds.), Handbook of mathematical functions with formulas, graphs and mathematical tables, National Bureau of Standards, Appl. Math. Ser. 55, 4th printing, Washington, 1965. – year: 1956 ident: b0005 article-title: Applied Analysis – year: 1962 ident: b0025 article-title: Approximate Calculation of Integrals – volume: 8 start-page: 287 year: 2005 end-page: 303 ident: b0035 article-title: General Euler–Boole’s and dual Euler–Boole’s formulas publication-title: Math. Inequal. Appl. – year: 1956 ident: 10.1016/j.amc.2010.11.002_b0005 – volume: 12 start-page: 573 issue: 3 year: 2009 ident: 10.1016/j.amc.2010.11.002_b0040 article-title: General closed 4-point quadrature formulae of Euler type publication-title: Math. Inequal. Appl. – ident: 10.1016/j.amc.2010.11.002_b0020 doi: 10.1115/1.3625776 – volume: 3 start-page: 337 issue: 3 year: 2000 ident: 10.1016/j.amc.2010.11.002_b0015 article-title: On generalizations of Ostrowski inequality via some Euler-type identities publication-title: Math. Inequal. Appl. – volume: 8 start-page: 287 issue: 2 year: 2005 ident: 10.1016/j.amc.2010.11.002_b0035 article-title: General Euler–Boole’s and dual Euler–Boole’s formulas publication-title: Math. Inequal. Appl. – volume: 45 start-page: E41 issue: E year: 2004 ident: 10.1016/j.amc.2010.11.002_b0010 article-title: A corrected quadrature formula and applications publication-title: ANZIAM J. – year: 1962 ident: 10.1016/j.amc.2010.11.002_b0025 – volume: 45 start-page: 355 issue: 3–4 year: 2007 ident: 10.1016/j.amc.2010.11.002_b0030 article-title: Quadrature formulas of Gauss type based on Euler identities publication-title: Math. Comput. Modelling doi: 10.1016/j.mcm.2006.05.009 |
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| Snippet | A family consisting of quadrature formulas which are exact for all polynomials of order ⩽5 is studied. Changing the coefficients, a second family of quadrature... A family consisting of quadrature formulas which are exact for all polynomials of order [inline image]5 is studied. Changing the coefficients, a second family... |
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| SubjectTerms | Algebra Bernoulli polynomials Closed 5-point quadrature formulas Computation Corrected quadrature formulas Derivatives Exact sciences and technology Extended Euler formulas Gauss formulas Intervals Lobatto formulas Mathematical analysis Mathematical models Mathematics Number theory Numerical analysis Numerical analysis. Scientific computation Quadratures Real functions Sciences and techniques of general use Sharp estimates of error |
| Title | On families of quadrature formulas based on Euler identities |
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