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].
@article{bwmeta1.element.doi-10_2478_s11533-012-0034-6,
author = {Bogus\l aw Bo\.zek and Wies\l aw Solak and Zbigniew Szyde\l ko},
title = {On some quadrature rules with Laplace end corrections},
journal = {Open Mathematics},
volume = {10},
year = {2012},
pages = {1172-1184},
zbl = {1248.65029},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0034-6}
}
Bogusław Bożek; Wiesław Solak; Zbigniew Szydełko. On some quadrature rules with Laplace end corrections. Open Mathematics, Tome 10 (2012) pp. 1172-1184. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0034-6/
[1] Bożek B., Solak W., Szydełko Z., On some quadrature rules with Gregory end corrections, Opuscula Math., 2009, 29(2), 117–129 | Zbl 1185.65045
[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 | Zbl 0992.65001
[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 | Zbl 0738.65009