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Sidi, Avram

Variable transformations and Gauss-Legendre quadrature for integrals with endpoint singularities. (English) Zbl 1209.65031

Math. Comput. 78, No. 267, 1593-1612 (2009).
The author studies the computation of integrals of functions \(f(x)\) that are enough differentiable in \((0,1)\) but have algebraic singularities at one or both of the endpoints \(x=0\) and \(x=1\), by combining a suitable variable transformation such that the transformed integrand has weaker singularities than those of \(f(x)\). He gives a computable representative of this class of methods and several numerical examples that confirm the theoretical results.
Reviewer: Antonio López-Carmona (Granada)

Cited in 3 Documents

MSC:

65D32 Numerical quadrature and cubature formulas
65B15 Euler-Maclaurin formula in numerical analysis
41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.)
41A55 Approximate quadratures

Keywords:

Gauss-Legendre quadrature; singular integrals; Euler-MacLaurin expansions; variable transformations; endpoint singularities; numerical examples
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References:

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[14] Avram Sidi, Asymptotic expansions of Gauss-Legendre quadrature rules for integrals with endpoint singularities, Math. Comp. 78 (2009), no. 265, 241 – 253. · Zbl 1198.65048
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