A novel class of symmetric and nonsymmetric periodizing variable transformations for numerical integration

DOI10.1007/s10915-006-9110-zzbMath1133.65013OpenAlexW2134633009WikidataQ120868215 ScholiaQ120868215MaRDI QIDQ2473338

Avram Sidi

Publication date: 27 February 2008

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10915-006-9110-z

zbMATH Keywords

numerical examplesquadrature formulaasymptotic expansionstrapezoidal rulevariable transformationsEuler-Maclaurin expansions

Mathematics Subject Classification ID

Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32) Euler-Maclaurin formula in numerical analysis (65B15)

Related Items (5)

Euler-Maclaurin expansions for integrals with arbitrary algebraic-logarithmic endpoint singularities ⋮ Further extension of a class of periodizing variable transformations for numerical integration ⋮ Variable transformations and Gauss–Legendre quadrature for integrals with endpoint singularities ⋮ \(\mathrm{PVTSI}^{(m)}\): a novel approach to computation of Hadamard finite parts of nonperiodic singular integrals ⋮ Euler–Maclaurin expansions for integrals with arbitrary algebraic endpoint singularities

Uses Software

• r2d2lri

Cites Work

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• Numerical integration over smooth surfaces in \(\mathbb R^3\) via class \(\mathcal I_{m}\) variable transformations. I: Smooth integrands
• Numerical integration over smooth surfaces in \(\mathbb R^3\) via class \(\mathcal Y_m\) variable transformations. II: Singular integrands
• Error expansions for multidimensional trapezoidal rules with Sidi transformations
• Quadrature of singular integrands over surfaces
• Analysis of Atkinson's variable transformation for numerical integration over smooth surfaces in \(\mathbb R^{3}\)
• Euler-Maclaurin expansions for integrals with endpoint singularities: A new perspective
• Numerical integration of functions with boundary singularities
• Quadrature over the sphere
• Application of class \(\mathcal I_{m}\) variable transformations to numerical integration over surfaces of spheres
• Practical Extrapolation Methods
• Semi-sigmoidal transformations for evaluating weakly singular boundary element integrals
• Algorithm 816: r2d2lri
• Extension of a class of periodizing variable transformations for numerical Integration

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