Further extension of a class of periodizing variable transformations for numerical integration

DOI10.1016/j.cam.2007.10.009zbMath1161.65019OpenAlexW1999901697MaRDI QIDQ950082

Avram Sidi

Publication date: 22 October 2008

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2007.10.009

zbMATH Keywords

numerical integrationasymptotic expansionsEuler-Maclaurin expansiontrapezoidal rulevariable transformationssin\(^m\)-transformation

Mathematics Subject Classification ID

Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32) Approximation to limiting values (summation of series, etc.) (40A25) Euler-Maclaurin formula in numerical analysis (65B15)

Related Items (7)

Euler-Maclaurin expansions for integrals with arbitrary algebraic-logarithmic endpoint singularities ⋮ Analysis of Atkinson's variable transformation for numerical integration over smooth surfaces in \(\mathbb R^{3}\) ⋮ Variable transformations and Gauss–Legendre quadrature for integrals with endpoint singularities ⋮ Fast automatic Bayesian cubature using lattice sampling ⋮ \(\mathrm{PVTSI}^{(m)}\): a novel approach to computation of Hadamard finite parts of nonperiodic singular integrals ⋮ Euler–Maclaurin expansions for integrals with arbitrary algebraic endpoint singularities ⋮ Application of class \(\mathcal I_{m}\) variable transformations to numerical integration over surfaces of spheres

Uses Software

• r2d2lri
• d2lri

Cites Work

• 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
• Euler-Maclaurin expansions for integrals with endpoint singularities: A new perspective
• \(d2lri\): A nonadaptive algorithm for two-dimensional cubature
• Numerical integration of functions with boundary singularities
• A novel class of symmetric and nonsymmetric periodizing variable transformations for numerical integration
• 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
• Development of non-linear transformations for improving convergence of sequences
• Algorithm 816: r2d2lri
• Extension of a class of periodizing variable transformations for numerical Integration
• On a Device for Computing the e m (S n ) Transformation
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