Abstract
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.
Supported by the Sofia University Research Fund under Contract 80-10-139/2018.
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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)
Avdzhieva, A., Nikolov, G.: Asymptotically optimal definite quadrature formulae of 4th order. J. Comput. Appl. Math. 311, 565–582 (2017)
Braß, H.: Quadraturverfahren. Vandenhoeck & Ruprecht, Göttingen (1977)
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)
Jetter, K.: Optimale Quadraturformeln mit semidefiniten Peano-Kernen. Numer. Math. 25, 239–249 (1976)
Köhler, P., Nikolov, G.: Error bounds for optimal definite quadrature formulae. J. Approx. Theory 81, 397–405 (1995)
Lange, G.: Beste und optimale definite Quadraturformel. Ph.D. Thesis, Technical University Clausthal, Germany (1977)
Lange, G.: Optimale definite Quadraturformel. In: Hämmerlin, G., (Ed.), Numerische Integration, ISNM vol. 45, Birkhäuser, Basel, Boston, Stuttgart, pp. 187–197 (1979)
Nikolov, G.: On certain definite quadrature formulae. J. Comput. Appl. Math. 75, 329–343 (1996)
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)
Schmeisser, G.: Optimale Quadraturformeln mit semidefiniten Kernen. Numer. Math. 20, 32–53 (1972)
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Avdzhieva, A., Gushev, V., Nikolov, G. (2019). Definite Quadrature Formulae of Order Three Based on the Compound Midpoint Rule. In: Nikolov, G., Kolkovska, N., Georgiev, K. (eds) Numerical Methods and Applications. NMA 2018. Lecture Notes in Computer Science(), vol 11189. Springer, Cham. https://doi.org/10.1007/978-3-030-10692-8_25
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DOI: https://doi.org/10.1007/978-3-030-10692-8_25
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