Richardson extrapolation for the iterated Galerkin solution of Urysohn integral equations with Green's kernels

@article{Rakshit2021RichardsonEF,
title={Richardson extrapolation for the iterated Galerkin solution of Urysohn integral equations with Green's kernels},
author={Gobinda Rakshit and Akshay S. Rane and Kshitij Patil},
journal={ArXiv},
year={2021},
volume={abs/2012.08879}
}
• Published 16 December 2020
• Mathematics
• ArXiv
We consider a Urysohn integral operator $\mathcal{K}$ with kernel of the type of Green's function. For $r \geq 1$, a space of piecewise polynomials of degree $\leq r-1$ with respect to a uniform partition is chosen to be the approximating space and the projection is chosen to be the orthogonal projection. Iterated Galerkin method is applied to the integral equation $x - \mathcal{K}(x) = f$. It is known that the order of convergence of the iterated Galerkin solution is $r+2$ and, at the above…

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