Nonlinear Extension of Multiproduct Expansion Schemes and Applications to Rigid Bodies
In this paper we discuss time integrators for nonlinear differential equations. In recent years, splitting approaches have become an important tool for reducing the computational time needed to solve differential equations. Moreover, nonlinearity is a challenge to splitting schemes, while one has to...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2013/681575 |
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| _version_ | 1832567229414113280 |
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| author | Jürgen Geiser |
| author_facet | Jürgen Geiser |
| author_sort | Jürgen Geiser |
| collection | DOAJ |
| description | In this paper we discuss time integrators for nonlinear differential equations. In recent years, splitting approaches have become an important tool for reducing the computational time needed to solve differential equations. Moreover, nonlinearity is a challenge to splitting schemes, while one has to extend the exp-functions in terms of a nonlinear Magnus expansion. Here we discuss a novel extension of the so-called multiproduct expansion methods, which is used to improve the standard Strang splitting schemes as to their nonlinearity. We present an extension of linear splitting schemes and concentrate on nonlinear systems of differential equations and generalise in this respect the recent MPE method; see (Chin and Geiser, 2011). Some first numerical examples, of rigid body problems, are given as benchmarks. |
| format | Article |
| id | doaj-art-526cbe2d653f48fb881227dcdcff0cb8 |
| institution | Kabale University |
| issn | 1687-9643 1687-9651 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-526cbe2d653f48fb881227dcdcff0cb82025-02-03T01:01:58ZengWileyInternational Journal of Differential Equations1687-96431687-96512013-01-01201310.1155/2013/681575681575Nonlinear Extension of Multiproduct Expansion Schemes and Applications to Rigid BodiesJürgen Geiser0University of Greifswald, Institute of Physics, Felix-Hausdorff-Str. 6, 17489 Greifswald, GermanyIn this paper we discuss time integrators for nonlinear differential equations. In recent years, splitting approaches have become an important tool for reducing the computational time needed to solve differential equations. Moreover, nonlinearity is a challenge to splitting schemes, while one has to extend the exp-functions in terms of a nonlinear Magnus expansion. Here we discuss a novel extension of the so-called multiproduct expansion methods, which is used to improve the standard Strang splitting schemes as to their nonlinearity. We present an extension of linear splitting schemes and concentrate on nonlinear systems of differential equations and generalise in this respect the recent MPE method; see (Chin and Geiser, 2011). Some first numerical examples, of rigid body problems, are given as benchmarks.http://dx.doi.org/10.1155/2013/681575 |
| spellingShingle | Jürgen Geiser Nonlinear Extension of Multiproduct Expansion Schemes and Applications to Rigid Bodies International Journal of Differential Equations |
| title | Nonlinear Extension of Multiproduct Expansion Schemes and Applications to Rigid Bodies |
| title_full | Nonlinear Extension of Multiproduct Expansion Schemes and Applications to Rigid Bodies |
| title_fullStr | Nonlinear Extension of Multiproduct Expansion Schemes and Applications to Rigid Bodies |
| title_full_unstemmed | Nonlinear Extension of Multiproduct Expansion Schemes and Applications to Rigid Bodies |
| title_short | Nonlinear Extension of Multiproduct Expansion Schemes and Applications to Rigid Bodies |
| title_sort | nonlinear extension of multiproduct expansion schemes and applications to rigid bodies |
| url | http://dx.doi.org/10.1155/2013/681575 |
| work_keys_str_mv | AT jurgengeiser nonlinearextensionofmultiproductexpansionschemesandapplicationstorigidbodies |