Jonathan Seyrich, Georgios Lukes-Gerakopoulos
By combining a standard symmetric, symplectic integrator scheme with a new step size controller, we provide an integration scheme that is symmetric, reversible and conserves the constant value of the Hamiltonian function, when the system is autonomous. This new scheme is appropriate for long lasting numerical integrations of geodesic orbits in spacetime backgrounds, whose corresponding Hamiltonian system is non-integrable, and, in general, for any non-integrable Hamiltonian system whose kinetic part depends on the position variables. We show by numerical examples that the new integrator is faster and more accurate i) than the standard symplectic integration schemes with or without standard adaptive step size controllers and ii) than an adaptive step Runge-Kutta scheme.
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http://arxiv.org/abs/1207.3175
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