  Motivated by numerically solving the Einstein field equations, we derive a
first-order reduction of the second-order $ f(T) $-teleparallel gravity field
equations in the pure-tetrad formulation (no spin connection). We then restrict
our attention to the teleparallel equivalent of general relativity (TEGR) and
propose a 3+1 decomposition of the governing equations that can be used in a
computational code. We demonstrate that for the matter-free space-time the
obtained system of first-order equations is equivalent to the tetrad
reformulation of general relativity by Estabrook, Robinson, Wahlquist, and
Buchman and Bardeen and therefore also admits a symmetric hyperbolic
formulation. The structure of the 3+1 equations resembles a lot of similarities
with the equations of relativistic electrodynamics and the recently proposed
dGREM tetrad-reformulation of general relativity.
