Definite Quadrature Formulae of Order Three Based on the Compound Midpoint Rule

  • Ana Avdzhieva
  • Vesselin Gushev
  • Geno NikolovEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11189)


A sequence of definite quadrature formulae of order three based on the compound midpoint rule is constructed. Their error constants are evaluated and simple a posteriori error estimates are derived.


Definite quadrature formulae Euler-Maclaurin summation formula Peano kernel A posteriori error estimate 


  1. 1.
    Avdzhieva, A., Gushev, V., Nikolov, G.: Definite quadrature formulae of order three with equidistant nodes. Ann. Univ. Sofia, Fac. Math. Inf. 104, 155–170 (2017)Google Scholar
  2. 2.
    Avdzhieva, A., Nikolov, G.: Asymptotically optimal definite quadrature formulae of 4th order. J. Comput. Appl. Math. 311, 565–582 (2017)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Braß, H.: Quadraturverfahren. Vandenhoeck & Ruprecht, Göttingen (1977)zbMATHGoogle Scholar
  4. 4.
    Förster, K.-J.: Survey on stopping rules in quadrature based on Peano kernel methods. Suppl. Rend. Circ. Math. Palermo, Ser. II 33, 311–330 (1993)MathSciNetzbMATHGoogle Scholar
  5. 5.
    Jetter, K.: Optimale Quadraturformeln mit semidefiniten Peano-Kernen. Numer. Math. 25, 239–249 (1976)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Köhler, P., Nikolov, G.: Error bounds for optimal definite quadrature formulae. J. Approx. Theory 81, 397–405 (1995)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Lange, G.: Beste und optimale definite Quadraturformel. Ph.D. Thesis, Technical University Clausthal, Germany (1977)Google Scholar
  8. 8.
    Lange, G.: Optimale definite Quadraturformel. In: Hämmerlin, G., (Ed.), Numerische Integration, ISNM vol. 45, Birkhäuser, Basel, Boston, Stuttgart, pp. 187–197 (1979)Google Scholar
  9. 9.
    Nikolov, G.: On certain definite quadrature formulae. J. Comput. Appl. Math. 75, 329–343 (1996)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Peano, G.: Resto nelle formule di quadratura espresso con un integrale definito. Atti della Reale Accademia dei Lincei Rendiconti (Ser. 5) 22, 562–569 (1913)zbMATHGoogle Scholar
  11. 11.
    Schmeisser, G.: Optimale Quadraturformeln mit semidefiniten Kernen. Numer. Math. 20, 32–53 (1972)MathSciNetCrossRefGoogle Scholar

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Authors and Affiliations

  1. 1.Faculty of Mathematics and InformaticsSofia University “St. Kliment Ohridski”SofiaBulgaria

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