Hybrid collocation methods for Fredholm integral equations with weakly singular kernels

DOI10.1016/j.apnum.2006.07.007zbMath1119.65122OpenAlexW2015622021MaRDI QIDQ881477

Min Huang, Yanzhao Cao, Yuesheng Xu, Liping Liu

Publication date: 30 May 2007

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2006.07.007

zbMATH Keywords

convergencenumerical examplessuperconvergenceround-off errorhybrid collocation methodsweakly singular Fredholm integral equations of second kind, Fredholm integro-differential equations

Mathematics Subject Classification ID

Integro-ordinary differential equations (45J05) Numerical methods for integral equations (65R20) Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) (45E10)

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Cites Work

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• Reconstruction and decomposition algorithms for biorthogonal multiwavelets
• A mathematical model of a biosensor
• Extrapolation method for Fredholm integral equations with non-smooth kernels
• Convergence of a discretization method for integro-differential equations
• On weakly singular Fredholm integral equations with displacement kernels
• Regularity of the solution to a class of weakly singular Fredholm integral equations of the second kind
• A wavelet algorithm for the solution of a singular integral equation over a smooth two-dimensional manifold
• Using the matrix refinement equation for the construction of wavelets on invariant sets
• Singularity preserving Galerkin methods for weakly singular Fredholm integral equations
• Wavelet Galerkin methods for second-kind integral equations
• Multi-level iteration methods for solving integral equations of the second kind
• Smoothing transformation and piecewise polynomial collocation for weakly singular Volterra integral equations
• Wavelet approximation methods for pseudodifferential equations. II: Matrix compression and fast solution
• Product integration methods for solving a system of nonlinear Volterra integral equations
• Variable transformations in the numerical solution of second kind Volterra integral equations with continuous and weakly singular kernels; extensions to Fredholm integral equations
• Superconvergence of the iterated hybrid collocation method for weakly singular Volterra integral equations
• A fast wavelet collocation method for integral equations on polygons
• Fast Algorithms for Classical Physics
• Superconvergence of the iterated degenerate kernel method
• Fast wavelet transforms and numerical algorithms I
• A multilevel augmentation method for solving ill-posed operator equations
• 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
• High order methods for weakly singular integral equations with nonsmooth input functions
• A construction of interpolating wavelets on invariant sets
• Gauss-Type Quadratures for Weakly Singular Integrals and their Application to Fredholm Integral Equations of the Second Kind
• Collocation methods for second-kind Volterra integral equations with weakly singular kernels
• Two-Grid Iteration Methods for Linear Integral Equations of the Second Kind on Piecewise Smooth Surfaces in $\mathbb{R}^3 $
• Numerical Solution of the Generalized Airfoil Equation for an Airfoil with a Flap
• The Petrov--Galerkin and Iterated Petrov--Galerkin Methods for Second-Kind Integral Equations
• Interpolation correction for collocation solutions of Fredholm integro-differential equations
• A Hybrid Collocation Method for Volterra Integral Equations with Weakly Singular Kernels
• Fast Collocation Methods for Second Kind Integral Equations
• Superconvergence of the Iterated Galerkin Methods for Hammerstein Equations
• Piecewise Polynomial Collocation for Fredholm Integro-Differential Equations with Weakly Singular Kernels
• The Numerical Solution of Fredholm integral Equations of the Second Kind
• A fast algorithm for particle simulations
• A multilevel method for solving operator equations
• Discrete wavelet Petrov--Galerkin methods