Asymptotic expressions for remainder terms of some quadrature rules

• Autorzy: Nenad Ujević , Nataša Bilić
• Języki publikacji: EN

Abstrakty

EN

Asymptotic expressions for remainder terms of the mid-point, trapezoid and Simpson’s rules are given. Corresponding formulas with finite sums are also given.

Słowa kluczowe

EN

quadrature rules; error terms; asymptotic expressions

Kategorie tematyczne

• 41A55: Approximate quadratures
• 41A80: Remainders in approximation formulas

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2008
• Tom: 6
• Numer: 4
• Strony: 559-567

Daty

wydano

2008-12-01

online

2008-10-08

Twórcy

autor

Nenad Ujević

autor

Nataša Bilić

Bibliografia

• [1] Cerone P., Dragomir S.S., Trapezoidal-type rules from an inequalities point of view, In: Handbook of analyticcomputational methods in applied mathematics, Anastassiou G. (Ed.), CRC Press, New York, 2000, 65–134
• [2] Cerone P., Dragomir S.S., Midpoint-type rules from an inequalities point of view, In: Handbook of analyticcomputational methods in applied mathematics, Anastassiou G. (Ed.), CRC Press, New York, 2000, 135–200
• [3] Cerone P., Three points rules in numerical integration, Nonlinear Anal., 2001, 47, 2341–2352 http://dx.doi.org/10.1016/S0362-546X(01)00358-3
• [4] Dragomir S.S., Agarwal R.P., Cerone P., On Simpson’s inequality and applications, J. Inequal. Appl., 2000, 5, 533–579 http://dx.doi.org/10.1155/S102558340000031X
• [5] Dragomir S.S., Cerone P., Roumeliotis J., A new generalization of Ostrowski’s integral inequality for mappings whose derivatives are bounded and applications in numerical integration and for special means, Appl. Math. Lett., 2000, 13, 19–25 http://dx.doi.org/10.1016/S0893-9659(99)00139-1
• [6] Dragomir S.S., Pečarić J., Wang S., The unified treatment of trapezoid, Simpson and Ostrowski type inequalities for monotonic mappings and applications, Math. Comput. Modelling, 2000, 31, 61–70 http://dx.doi.org/10.1016/S0895-7177(00)00046-7
• [7] Dragomir S.S., Rassias Th.M., Ostrowski type inequalities and applications in numerical integration, Kluwer Academic, 2002
• [8] Krommer A.R., Ueberhuber C.W., Computational integration, SIAM, Philadelphia, 1998
• [9] Pearce C.E.M., Pečarić J., Ujevic N., Varosanec S., Generalizations of some inequalities of Ostrowski-Gross type, Math. Inequal. Appl., 2000, 3, 25–34
• [10] Ujevic N., On perturbed mid-point and trapezoid inequalities and applications, Kyungpook Math. J., 2003, 43, 327–334
• [11] Ujevic N., A generalization of Ostrowski’s inequality and applications in numerical integration, Appl. Math. Lett., 2004, 17, 133–137 http://dx.doi.org/10.1016/S0893-9659(04)90023-7
• [12] Ujevic N., Roberts A.J., A corrected quadrature formula and applications, ANZIAM J., 2003, 45, 41–56
• [13] Whittaker E.T., Watson G.N., A course of modern analysis, Cambridge, 1996

Identyfikatory

DOI

10.2478/s11533-008-0050-8