We have developed a numerical model for the temporal evolution of particle and photon spectra resulting from nonthermal processes at the shock fronts formed in merging clusters of galaxies. Fermi acceleration is approximated by injecting power-law distributions of particles during a merger event, subject to constraints on maximum particle energies. We consider synchrotron, bremsstrahlung, Compton, and Coulomb processes for the electrons, nuclear, photomeson, and Coulomb processes for the protons, and knock-on electron production during the merging process. The broadband radio through $gamma$-ray emission radiated by nonthermal protons and primary and secondary electrons is calculated both during and after the merger event. To test the ability of the computer model to accurately calculate the nonthermal emission expected from a cluster merger event, we apply the model to the Coma cluster of galaxies, and show that the centrally located radio emission and the Hard X-ray excess observed at 40-80$kev$ is well fit by our model. If our model is correct, then the Coma cluster will be significantly detected with GLAST and ground-based air Cherenkov telescopes.
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