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Abstract: Understanding the behavior of a dynamical system is usually accomplished by visualization of its phase space portraits.
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In this contribution a class of geometry preserving integrators based on Lie-groups and -algebras is presented which preserve these geometric features exactly.
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Patrick R. Schmitt, Paul Steinmann: Geometrie Numerical Integration of Simple Dynamical Systems. Visualization of Large and Unstructured Data Sets 2007: ...
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The second edition is substantially revised and enlarged, with many improvements in the presentation and additions concerning in particular non-canonical Hamiltonian systems, highly oscillatory mechanical systems, and the dynamics of multistep methods.
Geometric numerical integration concerns the development, analysis, and use of algorithms for the numerical solution of differential equations.
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The course introduces some basic geometric numerical methods including the symplectic method for Hamiltonian systems, the volume-preserving method for ...
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Can we have the same property for the numerical solution? Simple Numerical Methods The most simple numerical method for the solution of ... Reich, Dynamical ...
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Symplectic integrators for Hamiltonian problems: an overview · Splitting methods · Geometric numerical integration illustrated by the Störmer–Verlet method.
2.1.3 Study: Linear Rotor Dynamics. In this study we illustrate the benefit of using geometric integration algorithms for a simple rotor dynamical problem.
The motivation of geometric numerical integration is not only to develop numerical methods with improved qualitative behavior but also to provide more accurate ...