Approximate solution of a singular integral equation using the Sobolev method

DOI10.1134/S1995080222050249zbMath1501.65159OpenAlexW4280574434MaRDI QIDQ2140967

D. M. Akhmedov, Kholmat Mahkambaevich Shadimetov

Publication date: 23 May 2022

Published in: Lobachevskii Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1995080222050249

zbMATH Keywords

Sobolev spaceweight functionsingular integral equationextremal functionoptimal coefficientsoptimal quadrature formulasCauchy type singular integral

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Numerical quadrature and cubature formulas (65D32) Integral equations with kernels of Cauchy type (45E05)

Related Items

Implicit upwind difference scheme for a symmetric \(t\)-hyperbolic system with variable coefficients and lowest terms

Cites Work

• The discrete analogue of a differential operator and its applications
• Approximating the singular integrals of Cauchy type with weight function on the interval
• On the convergence of spline product quadratures for Cauchy principal value integrals
• Proof of the numerical method of 'discrete vortices' for solving singular integral equations
• Optimal quadrature formulas for Cauchy type singular integrals in Sobolev space
• Gaussian quadrature formulae of the third kind for Cauchy principal value integrals: Basic properties and error estimates
• Optimal interpolation formulas in the space \(W_2^{(m,m-1)}\)
• Optimal quadrature formulas with derivatives for Cauchy type singular integrals
• Best Approximate Integration Formulas; Best Approximation Formulas
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item