A Non-Existence Result for Hamiltonian Integrators
P. F. Tupper · 2006 · arXiv
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Abstract (excerpt)
We consider the numerical simulation of Hamiltonian systems of ordinary differential equations. Two features of Hamiltonian systems are that energy is conserved along trajectories and phase space volume is preserved by the flow. We want to determine if there are integration schemes that preserve these two properties for all Hamiltonian systems, or at least for all systems in a wide class. This paper provides provides a negative result in the case of two dimensional (one degree of freedom) Hamiltonian systems, for which phase space volume is identical to area. Our main theorem shows that there
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Metadata source: arXiv