Quadrature rules with multiple nodes for evaluating integrals with strong singularities
Само за регистроване кориснике
2006
Чланак у часопису (Објављена верзија)
Метаподаци
Приказ свих података о документуАпстракт
We present a method based on the Chakalov–Popoviciu quadrature formula of Lobatto type, a rather general case of quadrature with multiple nodes, for approximating integrals defined by Cauchy principal values or by Hadamard finite parts. As a starting point we use the results obtained by L. Gori and E. Santi (cf. On the evaluation of Hilbert transforms by means of a particular class of Turán quadrature rules, Numer. Algorithms 10 (1995), 27–39; Quadrature rules based on
s-orthogonal polynomials for evaluating integrals with strong singularities, Oberwolfach Proceedings: Applications and Computation of Orthogonal Polynomials, ISNM 131, Birkhäuser, Basel, 1999, pp. 109–119). We generalize their results by using some of our numerical procedures for stable calculation of the quadrature formula with multiple nodes of Gaussian type and proposed methods for estimating the remainder term in such type of quadrature formulae. Numerical examples, illustrations and comparisons are also shown.
Кључне речи:
Quadratures with multiple nodes / sigma-orthogonal polynomials / Finite part integral in sense of Hadamard / Cauchy principal value / Remainder term for analytic functions / Contour integral representation / Error estimateИзвор:
Journal of Computational and Applied Mathematics, 2006, 189, 1-2, 689-702Издавач:
- Elsevier
Финансирање / пројекти:
- Serbian Ministry of Science and Environmental Protection
Институција/група
Mašinski fakultetTY - JOUR AU - Milovanović, Gradimir AU - Spalević, Miodrag PY - 2006 UR - https://machinery.mas.bg.ac.rs/handle/123456789/5072 AB - We present a method based on the Chakalov–Popoviciu quadrature formula of Lobatto type, a rather general case of quadrature with multiple nodes, for approximating integrals defined by Cauchy principal values or by Hadamard finite parts. As a starting point we use the results obtained by L. Gori and E. Santi (cf. On the evaluation of Hilbert transforms by means of a particular class of Turán quadrature rules, Numer. Algorithms 10 (1995), 27–39; Quadrature rules based on s-orthogonal polynomials for evaluating integrals with strong singularities, Oberwolfach Proceedings: Applications and Computation of Orthogonal Polynomials, ISNM 131, Birkhäuser, Basel, 1999, pp. 109–119). We generalize their results by using some of our numerical procedures for stable calculation of the quadrature formula with multiple nodes of Gaussian type and proposed methods for estimating the remainder term in such type of quadrature formulae. Numerical examples, illustrations and comparisons are also shown. PB - Elsevier T2 - Journal of Computational and Applied Mathematics T1 - Quadrature rules with multiple nodes for evaluating integrals with strong singularities EP - 702 IS - 1-2 SP - 689 VL - 189 UR - https://hdl.handle.net/21.15107/rcub_machinery_5072 ER -
@article{ author = "Milovanović, Gradimir and Spalević, Miodrag", year = "2006", abstract = "We present a method based on the Chakalov–Popoviciu quadrature formula of Lobatto type, a rather general case of quadrature with multiple nodes, for approximating integrals defined by Cauchy principal values or by Hadamard finite parts. As a starting point we use the results obtained by L. Gori and E. Santi (cf. On the evaluation of Hilbert transforms by means of a particular class of Turán quadrature rules, Numer. Algorithms 10 (1995), 27–39; Quadrature rules based on s-orthogonal polynomials for evaluating integrals with strong singularities, Oberwolfach Proceedings: Applications and Computation of Orthogonal Polynomials, ISNM 131, Birkhäuser, Basel, 1999, pp. 109–119). We generalize their results by using some of our numerical procedures for stable calculation of the quadrature formula with multiple nodes of Gaussian type and proposed methods for estimating the remainder term in such type of quadrature formulae. Numerical examples, illustrations and comparisons are also shown.", publisher = "Elsevier", journal = "Journal of Computational and Applied Mathematics", title = "Quadrature rules with multiple nodes for evaluating integrals with strong singularities", pages = "702-689", number = "1-2", volume = "189", url = "https://hdl.handle.net/21.15107/rcub_machinery_5072" }
Milovanović, G.,& Spalević, M.. (2006). Quadrature rules with multiple nodes for evaluating integrals with strong singularities. in Journal of Computational and Applied Mathematics Elsevier., 189(1-2), 689-702. https://hdl.handle.net/21.15107/rcub_machinery_5072
Milovanović G, Spalević M. Quadrature rules with multiple nodes for evaluating integrals with strong singularities. in Journal of Computational and Applied Mathematics. 2006;189(1-2):689-702. https://hdl.handle.net/21.15107/rcub_machinery_5072 .
Milovanović, Gradimir, Spalević, Miodrag, "Quadrature rules with multiple nodes for evaluating integrals with strong singularities" in Journal of Computational and Applied Mathematics, 189, no. 1-2 (2006):689-702, https://hdl.handle.net/21.15107/rcub_machinery_5072 .