Generalized Gaussian quadratures for integrals with logarithmic singularity | Zendy

Gradimir V. Milovanović | Zendy

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Generalized Gaussian quadratures for integrals with logarithmic singularity

Author(s) -

Gradimir V. Milovanović

Publication year - 2016

Publication title -

filomat

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.449

H-Index - 34

eISSN - 2406-0933

pISSN - 0354-5180

DOI - 10.2298/fil1604111m

Subject(s) - mathematics , gaussian quadrature , logarithm , gauss–laguerre quadrature , quadrature (astronomy) , clenshaw–curtis quadrature , gauss–kronrod quadrature formula , gravitational singularity , singularity , gauss–hermite quadrature , tanh sinh quadrature , gaussian , mathematical analysis , gauss–jacobi quadrature , numerical integration , pure mathematics , nyström method , integral equation , physics , quantum mechanics , engineering , electrical engineering

A short account on Gaussian quadrature rules for integrals with logarithmic singularity, as well as some new results for weighted Gaussian quadrature formulas with respect to generalized Gegenbauer weight $x\mapsto |x|^\gamma(1-x^2)^\alpha$, $\alpha,\gamma>-1$, on $(-1,1)$, which are appropriated for functions with and without logarithmic singularities, are considered. Methods for constructing such kind of quadrature formulas and some numerical examples are included.

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