On some quadrature rules with Laplace end corrections

• Autorzy: Bogusław Bożek , Wiesław Solak , Zbigniew Szydełko
• Języki publikacji: EN

Abstrakty

EN

We investigate quadrature rules with Laplace end corrections that depend on a parameter β. Specific values of β yield sixth order rules. We apply our results to approximating the sum of slowly converging series s = Σi=1∞ f(i + 1/2) where f ∈ C 6 with its sixth derivative of constant sign on [m, ∞) and ∫ m∞ f(x)dx is known for m ∈ ℕ. Several examples show the efficiency of this method. This paper continues the results from [Solak W., Szydełko Z., Quadrature rules with Gregory-Laplace end corrections, J. Comput. Appl. Math., 1991, 36(2), 251–253].

Słowa kluczowe

EN

Numerical integration; Quadrature formulas; Summation of series

Kategorie tematyczne

• 65B10: Summation of series
• 65G99: None of the above, but in this section
• 65D30: Numerical integration
• 65D32: Quadrature and cubature formulas

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2012
• Tom: 10
• Numer: 3
• Strony: 1172-1184

Daty

wydano

2012-06-01

online

2012-03-24

Twórcy

autor

Bogusław Bożek

• University of Science and Technology

autor

Wiesław Solak

• University of Science and Technology

autor

Zbigniew Szydełko

• University of Science and Technology

Bibliografia

• [1] Bożek B., Solak W., Szydełko Z., On some quadrature rules with Gregory end corrections, Opuscula Math., 2009, 29(2), 117–129
• [2] Kincaid D., Cheney W., Numerical Analysis, Brooks/Cole, Pacific Grove, 2002
• [3] Solak W., A remark on power series estimation via boundary corrections with parameter, Opuscula Math., 1999, 19, 75–80
• [4] Solak W., Szydełko Z., Quadrature rules with Gregory-Laplace end corrections, J. Comput. Appl. Math., 1991, 36(2), 251–253 http://dx.doi.org/10.1016/0377-0427(91)90031-E

Identyfikatory

DOI

10.2478/s11533-012-0034-6