Richardson extrapolation for the discrete iterated modified projection solution

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...

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Bibliographic Details
Published in:Numerical algorithms Vol. 85; no. 1; pp. 171 - 189
Main Authors: Kulkarni, Rekha P., Rakshit, Gobinda
Format: Journal Article
Language:English
Published: New York Springer US 01.09.2020
Springer Nature B.V
Subjects:
Algebra
Algorithms
Asymptotic series
Computer Science
Convergence
Extrapolation
Integral equations
Methods
Numeric Computing
Numerical Analysis
Original Paper
Polynomials
Quadratures
Theory of Computation
45G10
65R20
Richardson extrapolation
Nyström approximation
Interpolatory projection
65J15
Urysohn integral operator
Gauss points
ISSN:1017-1398, 1572-9265
Online Access:Get full text
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Summary: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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ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-019-00808-5