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Showing 1 to 7 of 7 for “"Symplectic integrators"”.
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Multi-Symplectic Integrators for Nonlinear Wave Equations
<p>Symplectic (area-preserving) integrators for Hamiltonian ordinary differential equations have shown to be robust, efficient and accurate in long-term calculations. In this thesis, we show how symplectic integrators have a natural generalization to Hamiltonian PDEs by introducing the concept of …
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Solving the N-body problem in astrophysics
… In the first part of this Thesis, I develop new symplectic integrators which provide a solution for the N-body problem. The integrators decompose the N-body problem into a superposition of two-body problems, which are integrable. Since they are symplectic, the integrators conserve all Poincaré …
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Explicit, Multi-Map Symplectic Integrator for Three -Body Classical Trajectory Studies in Hyperspherical Coordinates
Symplectic integrators are well known for preserving the phase space volume in Hamiltonian dynamics and are particularly suited for problems that require long integration times. There is a general operator splitting method for developing explicit symplectic integration algorithms to any arbitrary …
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Explicit, multi-map symplectic integrator for three-body classical trajectory studies in hyperspherical coordinates
Symplectic integrators are well known for preserving the phase space volume in Hamiltonian dynamics and are particularly suited for problems that require long integration times. There is a general operator splitting method for developing explicit symplectic integration algorithms to any arbitrary …
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Comparison of Second Order Conformal Symplectic Schemes with Linear Stability Analysis
… numerically. Each method is shown to preserve a symplectic form up to a constant and are therefore conformal symplectic integrators, with each method shown to accurately preserve the rate of momentum dissipation. An analytical linear stability analysis is completed for each method, establishing …
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Geometric Integrators for Hamiltonian PDEs
… which, as an ODE, possesses a highly nonlinear symplectic structure, For this system we consider a generating function approach to the nonstandard symplectic form, and derive novel symplectic integrators of arbitrary order exploiting the particular structure of AL where the standard techniques …