• DOI:10.1080/00207160.2021.1986215
• Corpus ID: 229205141

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}
}

• Gobinda Rakshit, Akshay S. Rane, Kshitij Patil
• 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 partition points it is $2r$. We obtain an asymptotic expansion of the iterated Galerkin solution at the partition points of the above Urysohn integral equation. Richardson extrapolation is used to improve the order of convergence. A numerical example is considered to illustrate our theoretical results.