Journal of Computational and Applied Mathematics
Wavelet applications to the Petrov--Galerkin method for Hammerstein equations
Applied Numerical Mathematics
Hybrid collocation methods for Fredholm integral equations with weakly singular kernels
Applied Numerical Mathematics
Iteration methods for Fredholm integral equations of the second kind
Computers & Mathematics with Applications
Richardson extrapolation of iterated discrete projection methods for eigenvalue approximation
Journal of Computational and Applied Mathematics
The use of Sherman-Morrison formula in the solution of Fredholm integral equation of second kind
Mathematics and Computers in Simulation
Higher-order finite volume methods for elliptic boundary value problems
Advances in Computational Mathematics
Mixed discretization schemes for electromagnetic surface integral equations
International Journal of Numerical Modelling: Electronic Networks, Devices and Fields
A fast solver for integral equations with convolution-type Kernel
Advances in Computational Mathematics
Iterated Fast Collocation Methods for Integral Equations of the Second Kind
Journal of Scientific Computing
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We develop in this paper a theoretical framework for the analysis of convergence for the Petrov-Galerkin method and superconvergence for the iterated Petrov--Galerkin method for Fredholm integral equations of the second kind. As important approaches to the analysis, we introduce notions of the generalized best approximation and the regular pair of trial space sequence and test space sequence. In Hilbert spaces, we characterize the regular pair in terms of the angle of two space sequences or the generalized best approximation projections. Several specific constructions of the Petrov--Galerkin elements for equations of both one dimension and two dimensions are presented and the convergence of the Petrov--Galerkin method and the iterated Petrov--Galerkin method using these elements is proved.