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Published in: Numerical Algorithms 1/2020

20-03-2020 | Original Paper

Richardson extrapolation for the discrete iterated modified projection solution

Authors: Rekha P. Kulkarni, Gobinda Rakshit

Published in: Numerical Algorithms | Issue 1/2020

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Abstract

Approximate solutions of Urysohn integral equations using projection methods involve integrals which need to be evaluated using a numerical quadrature formula. It gives rise to the discrete versions of the projection methods. For r ≥ 1, a space of piecewise polynomials of degree ≤ r − 1 with respect to an uniform partition is chosen to be the approximating space and the projection is chosen to be the interpolatory projection at r Gauss points. Asymptotic expansion for the iterated modified projection solution is available in literature. In this paper, we obtain an asymptotic expansion for the discrete iterated modified projection solution and use Richardson extrapolation to improve the order of convergence. Our results indicate a choice of a numerical quadrature which preserves the order of convergence in the continuous case. Numerical results are given for a specific example.

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Metadata
Title
Richardson extrapolation for the discrete iterated modified projection solution
Authors
Rekha P. Kulkarni
Gobinda Rakshit
Publication date
20-03-2020
Publisher
Springer US
Published in
Numerical Algorithms / Issue 1/2020
Print ISSN: 1017-1398
Electronic ISSN: 1572-9265
DOI
https://doi.org/10.1007/s11075-019-00808-5

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