On the convergence of spline product quadratures for Cauchy principal value integrals

DOI10.1016/0377-0427(91)90025-FzbMath0738.65007MaRDI QIDQ1177200

Elisabetta Santi, Cattarina Dagnino

Publication date: 26 June 1992

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

zbMATH Keywords

convergence ratescubic splineCauchy principal value integralsJacobi weightproduct integration formulasspline product quadratures

Mathematics Subject Classification ID

Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane (30E20) Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32)

Related Items (12)

Numerical integration based on quasi-interpolating splines ⋮ Approximate solution of a singular integral equation using the Sobolev method ⋮ On the uniform convergence of Cauchy principal values of quasi-interpolating splines ⋮ On the evaluation of Cauchy principal value integrals by rules based on quasi-interpolating splines ⋮ Constructing solutions of Cauchy type integral equations by using four kinds of basis ⋮ Numerical integration based on bivariate quadratic spline quasi-interpolants on Powell-Sabin partitions ⋮ Passive Approximation and Optimization Using B-splines ⋮ Limits of calculating the finite Hilbert transform from discrete samples ⋮ A quadrature rule of interpolatory type for Cauchy integrals ⋮ Quadrature formula for approximating the singular integral of Cauchy type with unbounded weight function on the edges ⋮ Numerical integration based on approximating splines ⋮ An algorithm for numerical integration based on quasi-interpolating splines

Cites Work

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• Gauss Type Quadrature Rules for Cauchy Principal Value Integrals
• Cubic Splines and Approximate Solution of Singular Integral Equations
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• On the Uniform Convergence of Gaussian Quadrature Rules for Cauchy Principal Value Integrals and Their Derivatives
• Piecewise-Polynomial Quadratures for Cauchy Singular Integrals
• On the Convergence of an Interpolatory Product Rule for Evaluating Cauchy Principal Value Integrals
• Approximation by spline interpolating bases
• Noninterpolatory Integration Rules for Cauchy Principal Value Integrals

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