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Dynamical Systems, Numerical Integration, and Exponentially Small Estimates

Please always quote using this URN: urn:nbn:de:0297-zib-3622
  • Dynamical systems with two well-separated time-scales are investigated using normal form theory. Exponential estimates for the normal form truncation error are derived and applied to the numerical integration of differential equations (backward error analysis) and the reduction of highly oscillatory Hamiltonian systems (constrained dynamics and correcting potentials). The theoretical results are used to formulate new algorithms for the time integration of conservative Hamiltonian systems (projected multiple time stepping, soft constraints, rigid bodies, symplectic variable step-size methods).

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Metadaten
Author:Sebastian Reich
Document Type:Habilitation
MSC-Classification:65-XX NUMERICAL ANALYSIS / 65Lxx Ordinary differential equations / 65L05 Initial value problems
CCS-Classification:G. Mathematics of Computing / G.1 NUMERICAL ANALYSIS / G.1.7 Ordinary Differential Equations
Date of first Publication:1998/07/08
Series (Serial Number):ZIB-Report (SC-98-19)
ZIB-Reportnumber:SC-98-19
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