Adaptive Time-Stepping. Part II. Time transformations applied to reversible Hamiltonian dynamics and weakly dissipative systems

2018. September 20. 10:15 to 11:00
H building, Room 607
Institute of Mathematics

Lecturer: Gustaf Söderlind (Lund University, Sweden)

In the second talk on time step adaptivity, we focus on the special needs of conservative dynamical systems. This includes Hamiltonian problems, and weakly dissipative systems. In integrable Hamiltonian problems, the mathematical solution is time reversible, which precludes the use of classical controllers, which adapt the step size to manage the error observed in previous steps. Instead, a time reversible tracking algorithm is developed, which allows full reversibility of the adaptive computational process. This is shown to preserve first integrals over long times, and even improves the accuracy over constant step size symplectic integrators. We demonstrate the procedure in two examples from celestial mechanics, and then proceed to demonstrate how a similar approach can be combined with splitting methods in weakly dissipative systems. The latter approach has been put to effective use in rolling bearing dynamic simulation.

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