Applying explicit symplectic-like methods to nonconservative nonseparable systems
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Extended phase-space explicit symplectic-like integrators were recently developed for nonseparable Hamiltonian systems. Following this idea, we establish numerical integration codes about the explicit symplectic-like algorithms for nonconservative nonseparable problems with velocity-dependent interaction forces, such as a damped harmonic oscillator and the orbital motion of a dust particle experiencing Poynting-Robertson drag. We use integral invariant relations of these nonconservative energies as accuracy checks in numerical integrations. It is found that these explicit symplectic-like methods still make the energy errors remain bounded in the nonconservative case. It is shown that the explicit symplectic-like integrators with the midpoint permutations are superior to those with the sequence two permutations of momenta and coordinates in the numerical accuracy although the latter algorithm is efficiently applicable to these dissipative systems.
- 1.E. Hairer, C. Lubich, G. Wanner, Geometric Numerical Integration (Springer, Berlin, 1999)Google Scholar