On the collocation methods for singular integral equations with Hilbert kernel

DOI10.1090/S0025-5718-08-02182-0zbMath1198.65054OpenAlexW2090691575MaRDI QIDQ3055124

Jinyuan Du

Publication date: 7 November 2010

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

Full work available at URL: https://doi.org/10.1090/s0025-5718-08-02182-0

zbMATH Keywords

collocation methodsdiscretization matricesHilbert singular integral operatorsHilbert singular quadrature operatorssingular integral equations with Hilbert kernel

Mathematics Subject Classification ID

Trigonometric approximation (42A10) General theory of numerical methods in complex analysis (potential theory, etc.) (65E05) Numerical solutions to equations with linear operators (65J10) Approximate quadratures (41A55)

Related Items (6)

Unnamed Item ⋮ Periodic Riemann boundary value problem ⋮ A note on the alternate trapezoidal quadrature method for Fredholm integral eigenvalue problems ⋮ A fast solver for the Hilbert-type singular integral equations based on the direct Fourier spectral method ⋮ \(L_2\) error estimates of collocation methods for solving certain singular integral equations ⋮ Riemann–Hilbert problems with Carleman shift and conjugation for polynomial Beltrami equations

Cites Work

• Projection methods for singular integral equations
• Recent developments in the numerical solution of singular integral equations
• Quadrature formulas of quasi-interpolation type for singular integrals with Hilbert kernel
• The modified quadrature method for classical pseudodifferential equations of negative order on smooth closed curves
• On trigonometric and paratrigonometric Hermite interpolation
• A natural interpolation formula for the numerical solution of singular integral equations with Hilbert kernel
• Rates of Convergence for the Method of Classical Collocation for Solving Singular Integral Equations
• A Galerkin-Petrov method for singular integral equations
• A convergence theorem for singular integral equations
• The Classical Collocation Method for Singular Integral Equations
• A General Theory for the Approximate Solution of Operator Equations of the Second Kind
• Numerical Quadrature of Periodic Singular Integral Equations
• Orthogonal Polynomials Associated with Singular Integral Equations Having a Cauchy Kernel
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