Iteration methods for Fredholm integral equations of the second kind

Authors:
Guangqing Long;Gnaneshwar Nelakanti
Affiliations:
Department of Mathematics, Guangxi Normal College, Nanning 530001, PR China and Department of Scientific Computing and Computer Applications, Sun Yat-sen University, Guangzhou 510275, PR China;Department of Scientific Computing and Computer Applications, Sun Yat-sen University, Guangzhou 510275, PR China and Department of Mathematics, Indian Institute of Technology, Kharagpur-721302, We ...
Venue:
Computers & Mathematics with Applications
Year:
2007

Citing 3
Cited 2

Superconvergence of the iterated Galerkin methods for Hammerstein equations

SIAM Journal on Numerical Analysis
The Petrov--Galerkin and Iterated Petrov--Galerkin Methods for Second-Kind Integral Equations

SIAM Journal on Numerical Analysis
Fast Collocation Methods for Second Kind Integral Equations

SIAM Journal on Numerical Analysis

Iterated fast multiscale Galerkin methods for Fredholm integral equations of second kind with weakly singular kernels

Applied Numerical Mathematics
Original article: Iteration methods for Fredholm integral equations of the second kind based on spline quasi-interpolants

Mathematics and Computers in Simulation

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Abstract

In this paper, we propose an efficient iteration algorithm for Fredholm integral equations of the second kind. We show that for every step of iteration the coefficient matrix of the linear system to be inverted remains the same as in the original approximation methods, while we obtain the superconvergence rates for every step of iteration. We apply our iteration methods to various approximation methods such as degenerate kernel methods, Galerkin, collocation and new projection methods. We illustrate our results by numerical experiments.