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Journal of Applied Mathematics
Volume 2014, Article ID 812137, 12 pages
http://dx.doi.org/10.1155/2014/812137
Research Article

Iterative Splitting Methods for Integrodifferential Equations: Theory and Applications

Department of Physics, Ernst-Moritz-Arndt University of Greifswald, Domstraße 14, 17487 Greifswald, Germany

Received 30 May 2014; Revised 5 August 2014; Accepted 5 August 2014; Published 24 August 2014

Academic Editor: Giuseppe Marino

Copyright © 2014 Jürgen Geiser. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We present novel iterative splitting methods to solve integrodifferential equations. Such integrodifferential equations are applied, for example, in scattering problems of plasma simulations. We concentrate on a linearised integral part and a reformulation to a system of first order differential equations. Such modifications allow for applying standard iterative splitting schemes and for extending the schemes, respecting the integral operator. A numerical analysis is presented of the system of semidiscretised differential equations as abstract Cauchy problems. In the applications, we present benchmark and initial realistic applications to transport problems with scattering terms. We also discuss the benefits of such iterative schemes as fast solver methods.