Computational methods for integral equations
Computational methods for integral equations
Introduction to numerical analysis: 2nd edition
Introduction to numerical analysis: 2nd edition
Extrapolation of the iterated—collocation method for integral equations of the second kind
SIAM Journal on Numerical Analysis
Integral equations: theory and numerical treatment
Integral equations: theory and numerical treatment
The Petrov--Galerkin and Iterated Petrov--Galerkin Methods for Second-Kind Integral Equations
SIAM Journal on Numerical Analysis
Richardson extrapolation of iterated discrete projection methods for eigenvalue approximation
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
A Finite Element Splitting Extrapolation for Second Order Hyperbolic Equations
SIAM Journal on Scientific Computing
Solutions of two-dimensional integral equation systems by using differential transform method
AMERICAN-MATH'11/CEA'11 Proceedings of the 2011 American conference on applied mathematics and the 5th WSEAS international conference on Computer engineering and applications
Computers & Mathematics with Applications
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
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In this paper, we study the numerical solution of two-dimensional Fredholm integral equation by discrete Galerkin and iterated discrete Galerkin method. We are able to derive an asymptotic error expansion of the iterated discrete Galerkin solution. This expansion covers arbitrarily high powers of the discretization parameters if the solution of the integral equation is smooth. The expansion gives rise to Richardson-type extrapolation schemes which rapidly improve the original rate of the convergence. Numerical experiments confirm our theoretical results.