Cubature formulae for nearly singular and highly oscillating integrals

DOI10.1007/s10092-018-0243-xOpenAlexW2792829422MaRDI QIDQ1742972

Donatella Occorsio, Giada Serafini

Publication date: 12 April 2018

Published in: Calcolo (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10092-018-0243-x

zbMATH Keywords

orthogonal polynomialscubature rulesapproximation by polynomials

Mathematics Subject Classification ID

Interpolation in approximation theory (41A05) Approximation by polynomials (41A10) Numerical quadrature and cubature formulas (65D32)

Related Items (8)

Numerical treatment of the generalized Love integral equation ⋮ A kernel-independent sum-of-exponentials method ⋮ HSMA: an \(O(N)\) electrostatics package implemented in LAMMPS ⋮ Product integration rules by the constrained mock-Chebyshev least squares operator ⋮ Volterra integral equations with highly oscillatory kernels: a new numerical method with applications ⋮ Cubature rules based on bivariate spline quasi-interpolation for weakly singular integrals ⋮ On product integration rules for highly oscillatory integrals on a triangle ⋮ A product integration rule on equispaced nodes for highly oscillating integrals

Uses Software

• Padua2DM
• Padua2D

Cites Work

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• \texttt{Padua2DM}: Fast interpolation and cubature at the Padua points in \texttt{MATLAB/Octave}
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• The numerical treatment of Love's integral equation having very small parameter
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• Algebraic cubature by linear blending of elliptical arcs
• Nyström method for Fredholm integral equations of the second kind in two variables on a triangle
• On Gauss–Lobatto Integration on the Triangle
• Modified Moments and Orthogonal Rational Functions
• Interpolation Processes
• A sinh transformation for evaluating two-dimensional nearly singular boundary element integrals
• The Construction of cubature rules for multivariate highly oscillatory integrals
• Mean Convergence of Lagrange Interpolation. III
• A fast algorithm for the construction of recurrence relations for modified moments
• A polynomial collocation method for the numerical solution of weakly singular and singular integral equations on non-smooth boundaries
• On the Construction of Gaussian Quadrature Rules from Modified Moments

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