On some quadrature rules with Laplace end corrections

Bogusław Bożek; Wiesław Solak; Zbigniew Szydełko

Open Mathematics (2012)

  • Volume: 10, Issue: 3, page 1172-1184
  • ISSN: 2391-5455

Abstract

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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].

How to cite

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Bogusław Bożek, Wiesław Solak, and Zbigniew Szydełko. "On some quadrature rules with Laplace end corrections." Open Mathematics 10.3 (2012): 1172-1184. <http://eudml.org/doc/269076>.

@article{BogusławBożek2012,
abstract = {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].},
author = {Bogusław Bożek, Wiesław Solak, Zbigniew Szydełko},
journal = {Open Mathematics},
keywords = {Numerical integration; Quadrature formulas; Summation of series; summation of series; quadrature formula of Laplace type; numerical examples},
language = {eng},
number = {3},
pages = {1172-1184},
title = {On some quadrature rules with Laplace end corrections},
url = {http://eudml.org/doc/269076},
volume = {10},
year = {2012},
}

TY - JOUR
AU - Bogusław Bożek
AU - Wiesław Solak
AU - Zbigniew Szydełko
TI - On some quadrature rules with Laplace end corrections
JO - Open Mathematics
PY - 2012
VL - 10
IS - 3
SP - 1172
EP - 1184
AB - 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].
LA - eng
KW - Numerical integration; Quadrature formulas; Summation of series; summation of series; quadrature formula of Laplace type; numerical examples
UR - http://eudml.org/doc/269076
ER -

References

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  1. [1] Bożek B., Solak W., Szydełko Z., On some quadrature rules with Gregory end corrections, Opuscula Math., 2009, 29(2), 117–129 Zbl1185.65045
  2. [2] Kincaid D., Cheney W., Numerical Analysis, Brooks/Cole, Pacific Grove, 2002 
  3. [3] Solak W., A remark on power series estimation via boundary corrections with parameter, Opuscula Math., 1999, 19, 75–80 Zbl0992.65001
  4. [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 Zbl0738.65009

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