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Winter 2020 Asymptotic expansion of iterated Galerkin solution of Fredholm integral equations of the second kind with Green's kernel
Gobinda Rakshit, Akshay S. Rane
J. Integral Equations Applications 32(4): 495-507 (Winter 2020). DOI: 10.1216/jie.2020.32.495

Abstract

We consider a Fredholm integral equation of the second kind with kernel of the type of Green’s function. Iterated Galerkin method is applied to such an integral equation. For r1, a space of piecewise polynomials of degree r1 with respect to a uniform partition is chosen to be the approximating space. We obtain an asymptotic expansion for the iterated Galerkin solution at the partition points. Richardson extrapolation is used to increase the order of convergence. A numerical example is considered to illustrate our theoretical results.

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Gobinda Rakshit. Akshay S. Rane. "Asymptotic expansion of iterated Galerkin solution of Fredholm integral equations of the second kind with Green's kernel." J. Integral Equations Applications 32 (4) 495 - 507, Winter 2020. https://doi.org/10.1216/jie.2020.32.495

Information

Received: 1 October 2019; Revised: 3 January 2020; Accepted: 11 February 2020; Published: Winter 2020
First available in Project Euclid: 5 January 2021

Digital Object Identifier: 10.1216/jie.2020.32.495

Subjects:
Primary: 45B05, 65B05, 65R20

Rights: Copyright © 2020 Rocky Mountain Mathematics Consortium

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Vol.32 • No. 4 • Winter 2020
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