Iterative Splitting Methods for Integrodifferential Equations: Theory and Applications
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 equ...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/812137 |
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| _version_ | 1832549447651819520 |
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| author | Jürgen Geiser |
| author_facet | Jürgen Geiser |
| author_sort | Jürgen Geiser |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-7e9ba3500cd6407ab40d1fe75eb264ca |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-7e9ba3500cd6407ab40d1fe75eb264ca2025-02-03T06:11:14ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/812137812137Iterative Splitting Methods for Integrodifferential Equations: Theory and ApplicationsJürgen Geiser0Department of Physics, Ernst-Moritz-Arndt University of Greifswald, Domstraße 14, 17487 Greifswald, GermanyWe 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.http://dx.doi.org/10.1155/2014/812137 |
| spellingShingle | Jürgen Geiser Iterative Splitting Methods for Integrodifferential Equations: Theory and Applications Journal of Applied Mathematics |
| title | Iterative Splitting Methods for Integrodifferential Equations: Theory and Applications |
| title_full | Iterative Splitting Methods for Integrodifferential Equations: Theory and Applications |
| title_fullStr | Iterative Splitting Methods for Integrodifferential Equations: Theory and Applications |
| title_full_unstemmed | Iterative Splitting Methods for Integrodifferential Equations: Theory and Applications |
| title_short | Iterative Splitting Methods for Integrodifferential Equations: Theory and Applications |
| title_sort | iterative splitting methods for integrodifferential equations theory and applications |
| url | http://dx.doi.org/10.1155/2014/812137 |
| work_keys_str_mv | AT jurgengeiser iterativesplittingmethodsforintegrodifferentialequationstheoryandapplications |