NEW ALGORITHM FOR MIXMASTER DYNAMICS

We present a new numerical algorithm for evolving the Mixmaster spacet imes. By using symplectic integration techniques to take advantage of the exact Taub solution for the scattering between asymptotic Kasner r egimes, we evolve these spacetimes with higher accuracy using much lar ger time steps than previously possible. The longer Mixmaster evolutio n thus allowed:a detailed comparison with the Belinskii-Khalatnikov-Li fshitz (BKL) approximate Mixmaster dynamics. In particular, we show th at errors between the BKL prediction and the measured parameters early in the simulation can be eliminated by relaxing the BKL assumptions t o yield an improved map. The improved map has different predictions fo r vacuum Bianchi type 1X and magnetic Bianchi type VI0 Mixmaster model s which are clearly matched in the simulation.