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Numerical solution of a non-linear Volterra integral equation


Maleknejad, Khosrow; Torabi, Parvin; Sauter, Stefan A (2016). Numerical solution of a non-linear Volterra integral equation. Vietnam Journal of Mathematics, 44(1):5-28.

Abstract

In this paper, a numerical method to solve non-linear integral equations based on a successive approximation technique is considered. A sequence of functions is produced which converges to the solution. The process includes a fixed point method, a quadrature rule, and an interpolation method. To find a total bound of the error, we investigate error bounds for each approximation and by combining them, we will derive an estimate for the total error. The accuracy and efficiency of the method is illustrated in some numerical examples.

Abstract

In this paper, a numerical method to solve non-linear integral equations based on a successive approximation technique is considered. A sequence of functions is produced which converges to the solution. The process includes a fixed point method, a quadrature rule, and an interpolation method. To find a total bound of the error, we investigate error bounds for each approximation and by combining them, we will derive an estimate for the total error. The accuracy and efficiency of the method is illustrated in some numerical examples.

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Additional indexing

Item Type:Journal Article, not refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:June 2016
Deposited On:10 Aug 2016 08:17
Last Modified:31 Oct 2016 08:29
Publisher:Springer
ISSN:2305-221X
Publisher DOI:https://doi.org/10.1007/s10013-015-0149-8

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