Beam dynamics simulations along the end-to-end beamlines and storage ring of the E989 experiment are performed using COSY INFINITY. In particular, preparation of detailed high-order transport maps calculated with an 8th order Runge–Kutta integrator and Differential-Algebraic (DA) methods yield precise solutions of the beam optics ODEs that cover nonlinearities associated to the small but relevant imperfections of E989. The use of transport maps in COSY INFINITY permits fast particle tracking in contrast with conventional orbit-integration beam dynamics codes. These features are essential for detailed and high-statistics studies of the muon beam in the g-2 storage ring which consider high-order electric and magnetic multipole terms from the EQS design and measured magnetic field imperfections, respectively. Additionally, storage ring simulations utilize COSY INFINITY's rigorous and highly accurate treatment of fringe fields and effective field boundaries for the EQS and accounts for beam collimation during the scraping, transition, and production stages of the experiment. Symplectification is performed using COSY INFINITY's most accurate symplectification method Extended Poincaré (EXPO).