Geometric Numerical Integration: Structure Preserving Algorithms for Ordinary Differential Equations

By Ernst Hairer, Christian Lubich, Gerhard Wanner. 2004

3,892 citations recorded by the source corpus.

Subfields: Computational Mechanics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/1dcc52126295f93be869635504adcd680de05f3a

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In Computational Mechanics

In Numerical Analysis

Citations in the corpus

Properties and uses of the Wilson flow in lattice QCD (2010, neutral): “[10], for example).”
Lax‐Wendroff and Nyström methods for seismic modelling (2009, background): “This is because scheme (31) is a second-order symplectic algorithm and scheme (32) is a nonsymplectic algorithm and symplectic algorithms have slower error growth than nonsymplectic ones (Hairer et al. 2002).”
Modulated Fourier expansions and heterogeneous multiscale methods (2009, methodology): “In Numerical Analysis they were first employed by Hairer & Lubich 2000 and their application is gaining momentum, as witnessed by the list of references in the monograph by Hairer et al. 2006.”
Fourth-and sixth-order commutator-free Magnus integrators for linear and non-linear dynamical systems (2006, methodology): “... consuming part of the methods (although for this very simple problem it is not necessarily the case) and we use a time step h such that the whole integration is reached with 800 evaluations of the function f . The following fourth-order methods are compared: (i) the symplectic integrators given ”
Bayesian computation: a summary of the current state, and samples backwards and forwards (2015, methodology): “The practical implementation relies on a k -th order symplectic integrator (Hairer et al. 2006), most commonly on the second order leapfrog approximation that relies on a small step level (cid:12), updating p and θ via a modiﬁed Euler’s method called the leapfrog that is reversible and being…”
Dynamical Low-Rank Approximation (2007, methodology): “Figure 3.3 shows such a situation for an example constructed by the same principles as the example discussed above, yet with a time dependence of the form cos(t), for t ∈ [0, 10 ] and with e=1e−1.”
The scope and limits of simulation in automated reasoning (2016, background): “richer physics than a pendulum, such as fluid dynamics, these kinds of problems can arise in much more complex forms [6, 23].”