Legendre Galerkin method for weakly singular Fredholm integral equations and the corresponding eigenvalue problem

DOI10.1007/s12190-013-0658-0zbMath1300.65095OpenAlexW1996890002MaRDI QIDQ2511389

Bijaya Laxmi Panigrahi, Gnaneshwar Nelakanti

Publication date: 5 August 2014

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

Full work available at URL: https://doi.org/10.1007/s12190-013-0658-0

zbMATH Keywords

numerical exampleFredholm integral equationserror boundseigenvalue problemsweakly singular kernelcompact integral operatorLegendre Galerkin method

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) (45E10) Fredholm integral equations (45B05) Eigenvalue problems for integral equations (45C05)

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Cites Work

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• A fast collocation method for eigen-problems of weakly singular integral operators
• Superconvergence of Legendre projection methods for the eigenvalue problem of a compact integral operator
• On weakly singular Fredholm integral equations with displacement kernels
• Discrete polynomial-based Galerkin methods for Fredholm integral equations
• An implementation of fast wavelet Galerkin methods for integral equations of the second kind
• Product Integration in the Presence of a Singularity
• Product Integration for Weakly Singular Integral Equations
• A piecewise polynomial approximation to the solution of an integral equation with weakly singular kernel
• The properties of solutions of weakly singular integral equations
• Spectral Approximation for Compact Operators
• Spectral Methods and Their Applications
• Gauss-Type Quadratures for Weakly Singular Integrals and their Application to Fredholm Integral Equations of the Second Kind
• The Numerical Solution of Integral Equations of the Second Kind
• Linear integral equations