Forward and non-forward symplectic integrators in solving classical dynamics problems

Understand

Forward time step integrators are splitting algorithms with only positive splitting coefficients.

• When used in solving physical evolution equations, these positive coefficients correspond to positive time steps.
• Forward algorithms are essential for solving time-irreversible equations that cannot be evolved using backward time steps.
• However, forward integrators are also better in solving time-reversible equations of classical dynamics by tracking as closely as possible the physical trajectory.