  A new symplectic time-reversible algorithm for numerical integration of the
equations of motion in magnetic liquids is proposed. It is tested and applied
to molecular dynamics simulations of a Heisenberg spin fluid. We show that the
algorithm exactly conserves spin lengths and can be used with much larger time
steps than those inherent in standard predictor-corrector schemes. The results
obtained for time correlation functions demonstrate the evident dynamic
interplay between the liquid and magnetic subsystems.
