The Method of Successive Approximations (Neumann’s Series) of Volterra Integral Equation of the Second Kind
Pure and Applied Mathematics Journal
Volume 5, Issue 6, December 2016, Pages: 211-219
Received: Oct. 12, 2016; Accepted: Oct. 28, 2016; Published: Dec. 23, 2016
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Author
Teshome Bayleyegn Matebie, College of Natural Science, Department of Mathematics, Arba Minch University, Arba Minch, Ethiopia
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Abstract
In this paper, the solving of a class of both linear and nonlinear Volterra integral equations of the first kind is investigated. Here, by converting integral equation of the first kind to a linear equation of the second kind and the ordinary differential equation to integral equation we are going to solve the equation easily. The method of successive approximations (Neumann’s series) is applied to solve linear and nonlinear Volterra integral equation of the second kind. Some examples are presented to illustrate methods.
Keywords
Volterra Integral Equation, First Kind, Second Kind, Kernel, Method of Successive Approximations
To cite this article
Teshome Bayleyegn Matebie, The Method of Successive Approximations (Neumann’s Series) of Volterra Integral Equation of the Second Kind, Pure and Applied Mathematics Journal. Vol. 5, No. 6, 2016, pp. 211-219. doi: 10.11648/j.pamj.20160506.16
Copyright
Copyright © 2016 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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