In the context of system function modeling for magnetic particle imaging, computing fast and accurate approxima-tions to the time evolution of magnetic nanoparticles’ (MNPs) mean magnetic moment is a problem of interest. In a software toolbox we comprise algorithms and methods that can simulate Brownian and Néel relaxation of MNPs’ magnetic moments that can be used to obtain more accurate model-based system matrices than those relying on the so-called equilibrium model. We present and discuss results obtained with these implementations which are made available in the software toolbox under github.com/MagneticParticleImaging/MNPDynamics.jl to inspire further research in these directions.