2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/35693We describe a numerical approach to address the BKL conjecture that the generic cosmological singularity is locally Mixmaster-like. We consider application of a symplectic PDE solver to three models of increasing complexity--spatially homogeneous (vacuum) Mixmaster cosmologies where we compare the symplectic ODE solver to a Runge-Kutta one, the (plane symmetric, vacuum) Gowdy universe on $T^3 \times R$ whose dynamical degrees of freedom satisfy nonlinearly coupled PDE's in one spatial dimension and time, and U(1) symmetric, vacuum cosmologies on $T^3 \times R$ which are the simplest spatially inhomogeneous universes in which local Mixmaster dynamics is allowed.Based on lectures given at WE-Heraeus-Seminar on Relativity and Scientific Computing. 24 pages, Latex, 9 figures in separate file BHfigs.uu, uses psfig.texGeneral Relativity and Quantum Cosmologytext