| Geometric integration methods for general nonlinear dynamic equation based on Magnus and Fer expansions |
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| 引用本文： | ZHANG Suying , * and DENG Zichen ,.Geometric integration methods for general nonlinear dynamic equation based on Magnus and Fer expansions[J].自然科学进展(英文版),2005(4). |
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| 作者姓名： | ZHANG Suying * and DENG Zichen |
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| 作者单位： | 1. Department of Engineering Mechanics，Northwestern Polytechnical University，Xi'an 710072，China; 2. College of Physical Electronic Engineering，Shanxi University，Taiyuan 030006，China; 3. State Key Laboratory of Structural Analysis of Industrial Equipment，Dalian University of Technology，Dalian 116023，China |
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| 基金项目： | SupportedbytheNationalNaturalScienceFoundationofChina (GrantNos.10 3 72 0 84，10 472 0 5 9)，FokYingTungYouthTeacherFoundation(GrantNo .710 0 5 )，theDoctoralProgramFoundationofEducationMinistryofChina (GrantNo .2 0 0 10 6990 16)，theOpenFoundationofSt |
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| 摘 要： | Ithasbeenknownforalongtimethatthesolu tionofthefollowingdifferentialequation :U· =A(t)U , U(t0 ) =I ,(1)whereA (t)standsforasufficientlysmoothn×nmatrixorlinearoperator ,canlocallybewrittenintheform1]U(t ,t0 ) =eΩ(t,t0 ) ,(2 )whereΩisobtainedasaninfiniteseriesΩ(t ,t0 ) =∑∞k =1Ωk(t,t0 ) . (3)Eqs .(2 )and (3)constitutetheso calledMagnusex pansionofthesolutionofthedifferentialequation(1) .EachtermΩkintheseries (3)isamultiplein tegralofcombinationsofnestedcommutators ,anditcanbeobtain…
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