Spectral refinement using a new projection method

DOI10.1017/S1446181100013791zbMath1066.65062OpenAlexW2158808749MaRDI QIDQ4650589

Rekha P. Kulkarni, N. Gnaneshwar

Publication date: 18 February 2005

Published in: The ANZIAM Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s1446181100013791

zbMATH Keywords

convergenceBanach spacescomparison of methodsGalerkin methoderror estimatesnumerical exampleseigenvalue problemsspline spaceintegral operatorsorthogonal projectioncompact linear operatorsGauss pointsinterpolatory projectionsmooth kernelnumerical quadrature formulaSloan methoddiscontinuous piecewise polynomial spaceSpectral refinement schemes

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Eigenvalue problems for linear operators (47A75) Numerical solutions to equations with linear operators (65J10) Eigenvalue problems for integral equations (45C05)

Related Items (6)

Modified Galerkin method for Volterra-Fredholm-Hammerstein integral equations ⋮ Spectral refinement based on superconvergent Nyström and degenerate kernel methods ⋮ Modified projection and the iterated modified projection methods for nonlinear integral equations ⋮ A degenerate kernel method for eigenvalue problems of compact integral operators ⋮ Iteration methods for Fredholm integral equations of the second kind ⋮ Convergence analysis of Galerkin and multi-Galerkin methods for linear integral equations on half-line using Laguerre polynomials

Cites Work

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• Superconvergence of piecewise polynomial Galerkin approximations, for Fredholm integral equations of the second kind
• The Discrete Galerkin Method for Integral Equations
• A fixed point technique to refine a simple approximate eigenvalue and a corresponding eigenvector
• Optimal L ∞ Error Estimates for Galerkin Approximations to Solutions of Two-Point Boundary Value Problems
• Spectral Approximation for Compact Operators
• A Bound on the L ∞ -Norm of L 2 -Approximation by Splines in Terms of a Global Mesh Ratio
• A New Superconvergent Projection Method for Approximate Solutions of Eigenvalue Problems
• Collocation at Gaussian Points

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