Numerical integration over smooth surfaces in \(\mathbb R^3\) via class \(\mathcal I_{m}\) variable transformations. I: Smooth integrands

DOI10.1016/j.amc.2005.01.077zbMath1086.65022OpenAlexW1514183721MaRDI QIDQ814757

Avram Sidi

Publication date: 7 February 2006

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

Full work available at URL: https://doi.org/10.1016/j.amc.2005.01.077

zbMATH Keywords

numerical integrationvariable transformationnumerical examplesasymptotic expansionsEuler-MacLaurin expansionsintegration over smooth surfacesproduct trapezoidal rule

Mathematics Subject Classification ID

Multidimensional problems (41A63) Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32) Euler-Maclaurin formula in numerical analysis (65B15)

Related Items

Numerical integration over smooth surfaces in \(\mathbb R^3\) via class \(\mathcal Y_m\) variable transformations. II: Singular integrands, Extension of a class of periodizing variable transformations for numerical Integration, Further extension of a class of periodizing variable transformations for numerical integration, A novel class of symmetric and nonsymmetric periodizing variable transformations for numerical integration, Analysis of Atkinson's variable transformation for numerical integration over smooth surfaces in \(\mathbb R^{3}\), Application of class \(\mathcal I_{m}\) variable transformations to numerical integration over surfaces of spheres

Uses Software

• r2d2lri
• d2lri

Cites Work

• An IMT-type double exponential formula for numerical integration
• Error expansions for multidimensional trapezoidal rules with Sidi transformations
• Quadrature of singular integrands over surfaces
• On a certain quadrature formula
• Euler-Maclaurin expansions for integrals with endpoint singularities: A new perspective
• Periodizing transformations for numerical integration
• \(d2lri\): A nonadaptive algorithm for two-dimensional cubature
• Practical Extrapolation Methods
• Development of non-linear transformations for improving convergence of sequences
• Algorithm 816: r2d2lri
• Numerical Evaluation of High-Dimensional Integrals
• The Numerical Solution of Fredholm integral Equations of the Second Kind
• 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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