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math.NA2017★ 1 cited
Adaptive Hamiltonian Variational Integrators and Symplectic Accelerated Optimization
Valentin Duruisseaux, Jeremy Schmitt, Melvin Leok
It is well known that symplectic integrators lose their near energy preservation properties when variable step sizes are used. The most common approach to combine adaptive step siz…
math.NA2017
Lagrangian and Hamiltonian Taylor Variational Integrators
Jeremy Schmitt, Tatiana Shingel, Melvin Leok
In this paper, we present a variational integrator that is based on an approximation of the Euler--Lagrange boundary-value problem via Taylor's method. This can viewed as a special…