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Gauss quadrature rules for finite part integrals
Author(s) -
Tsamasphyros George,
Dimou George
Publication year - 1990
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620300103
Subject(s) - gauss–kronrod quadrature formula , gauss–jacobi quadrature , clenshaw–curtis quadrature , tanh sinh quadrature , mathematics , quadrature (astronomy) , gaussian quadrature , numerical integration , gauss–laguerre quadrature , gauss–hermite quadrature , weight function , gauss , mathematical analysis , orthogonal polynomials , nyström method , integral equation , physics , quantum mechanics , optics
We construct a set of polynomials φ n ( x ,ζ) which are orthogonal with respect to w ( x )/( x − ζ) 2 , where w x is a weight function. These polynomials can be used for the definition of a Gauss quadrature formula for the finite part integralThe process is exactly the same as the one used for the extraction of the classical Gauss formula for the Riemann integrals. Three different methods are derived. The first and most accurate quadrature formula is successfully tested in some numerical examples. The proposed quadrature formulas have many applications in problems of mathematical physics, mechanics, etc.