  Thermal non-equilibrium (TNE) is believed to be a potentially important
process in understanding some properties of the magnetically closed solar
corona. Through one-dimensional hydrodynamic models, this paper addresses the
importance of the numerical spatial resolution, footpoint heating timescales
and background heating on TNE. Inadequate transition region (TR) resolution can
lead to significant discrepancies in TNE cycle behaviour, with TNE being
suppressed in under-resolved loops. A convergence on the periodicity and plasma
properties associated with TNE required spatial resolutions of less than 2 km
for a loop of length 180 Mm. These numerical problems can be resolved using an
approximate method that models the TR as a discontinuity using a jump
condition, as proposed by Johnston et al. (2017a,b). The resolution
requirements (and so computational cost) are greatly reduced while retaining
good agreement with fully resolved results. Using this approximate method we
(i) identify different regimes for the response of coronal loops to
time-dependent footpoint heating including one where TNE does not arise and
(ii) demonstrate that TNE in a loop with footpoint heating is suppressed unless
the background heating is sufficiently small. The implications for the
generality of TNE are discussed.
