  We test a non-parametric higher-order Jeans analysis method, GravSphere, on
32 simulated dwarf galaxies comparable to classical Local Group dwarfs like
Fornax. The galaxies are selected from the APOSTLE suite of cosmological
hydrodynamics simulations with Cold Dark Matter (CDM) and Self-Interacting Dark
Matter (SIDM) models, allowing us to investigate cusps and cores in density
distributions. We find that, for CDM dwarfs, the recovered enclosed mass
profiles have a bias of no more than 10 per cent, with a 50 per cent scatter in
the inner regions and a 20 per cent scatter near the half-light radius,
consistent with standard mass estimators. The density profiles are also
recovered with a bias of no more than 10 per cent and a scatter of 30 per cent
in the inner regions. For SIDM dwarfs, the mass and density profiles are
recovered within our 95 per cent confidence intervals, but are biased towards
cuspy dark matter distributions. This is mainly due to a lack of sufficient
constraints from the data. We explore the sources of scatter in the accuracy of
the recovered profiles and suggest a $\chi^2$ statistic to separate successful
models from biased ones. Finally, we show that the uncertainties on the mass
profiles obtained with GravSphere are smaller than those for comparable Jeans
methods, and that they can be further improved if stronger priors, motivated by
cosmological simulations, are placed on the velocity anisotropy. We conclude
that GravSphere is a promising Jeans-based approach for modelling dark matter
distributions in dwarf galaxies.
