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We investigate the impact of using high-order numerical methods to study themerger of magnetised neutron stars with finite-temperature microphysics andneutrino cooling in full general relativity. By implementing a fourth-orderaccurate conservative finite-difference scheme we model the inspiral togetherwith the early post-merger and highlight the differences to traditionalsecond-order approaches at the various stages of the simulation. We find thateven for finite-temperature equations of state, convergence orders higher thansecond order can be achieved in the inspiral and post-merger for thegravitational-wave phase. We further demonstrate that the second-order schemeoverestimates the amount of proton-rich shock-heated ejecta, which can have animpact on the modelling of the dynamical part of the kilonova emission.Finally, we show that already at low resolution the growth rate of the magneticenergy is consistently resolved by using a fourth-order scheme.

Beyond second-order convergence in simulations of magnetised binary neutron stars with realistic microphysics