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Reaction Dissipative Particle Dynamics (DPD-RX) is a promising coarse-graining (CG) method for modeling energetic materials at the mesoscale. The LAMMPS DPD-RX multiscale-modeling software combines stochastic particle dynamics with intra-particle chemical kinetics. The chemical kinetics model requires the solution of a system of ordinary differential equations (ODEs) within each CG particle at each time step. The ODE solutions are computationally intensive and exceed 99 of the run time for some cases. Several acceleration methods were tested for the chemical kinetics DPD-RX component including different ODE solver methods (implicit vs. explicit), parallel programming paradigms (MPI vs. OpenMP vs. GPU), and matrix storage representations (dense vs. sparse). For a small, reduced-order reaction mechanism, the best acceleration was 6.1 times. For a larger, more chemically detailed mechanism, the best acceleration exceeded 60 times the baseline performance. This level of acceleration enables the use of higher fidelity reaction mechanisms, which have a broader modeling applicability.