  The lattice provides a powerful tool to non-perturbatively investigate
strongly coupled supersymmetric Yang-Mills (SYM) theories. The pure SU(2) SYM
theory with one supercharge is simulated on large lattices with small Majorana
gluino masses down to about $am_{\tilde g}=0.068$ with lattice spacing $a\simeq
0.125$ fm. The gluino dynamics is simulated by the Two-Step Multi-Boson (TSMB)
and the Two-Step Polynomial Hybrid Monte Carlo (TS-PHMC) algorithms.
Supersymmetry (SUSY) is broken explicitly by the lattice and the Wilson term
and softly by the presence of a non-vanishing gluino mass. However, the
recovery of SUSY is expected in the infinite volume continuum limit by tuning
the bare parameters to the SUSY point in the parameter space. This scenario is
studied by the determination of the low-energy mass spectrum and by means of
lattice SUSY Ward-Identities (WIs).
