  We describe the application of pseudo-spectral methods to problems of
holographic thermal quenches of relevant couplings in strongly coupled gauge
theories. We focus on quenches of a fermionic mass term in a strongly coupled
N=4 supersymmetric Yang-Mills plasma, and the subsequent equilibration of the
system. From the dual gravitational perspective, we study the gravitational
collapse of a massive scalar field in asymptotically anti-de Sitter geometry
with a prescribed boundary condition for its non-normalizable mode. Access to
the full background geometry of the gravitational collapse allows for the study
of nonlocal probes of the thermalization process. We discuss the evolution of
the apparent and the event horizons, the two-point correlation functions of
operators of large conformal dimensions, and the evolution of the entanglement
entropy of the system. We compare the thermalization process from the viewpoint
of local (the one-point) correlation functions and these nonlocal probes,
finding that the thermalization time as measured by the probes is length
dependent, and approaches the thermalization time of the one-point function for
longer probes. We further discuss how the different energy scales of the
problem contribute to its thermalization.
