Quadrature rules with multiple nodes for evaluating integrals with strong singularities

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:189

Article; Proceedings Paper

Milovanovic, GV ; Spalevic, MM

关键词: 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 estimate;   

DOI  :  10.1016/j.cam.2005.05.021

来源: Elsevier

【 摘 要 】

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 Turan 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, Birkhauser, 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. (c) 2005 Elsevier B.V. All rights reserved.

【 授权许可】

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