Starting with the Mean Field Method (MFM) and Boundary Element Method (BEM), we investigate a mathematical model based on these two methods for studying particle-coarsening process in alloys. With MFM, second-phase particles are considered to be merged into bulk matrix, which greatly simplifies computation. However, the Mean-Field model itself is limited to a system with extremely small volume fractions of second phase. By combining BEM with MFM, this mathematical model shows the influence of second phase in particle-coarsening process. Our primary work demonstrates the robustness and capability of this model. This model is however limited to particle coarsening that is far away from grain boundaries. In this dissertation, we successfully extend the model to particle coarsening near grain boundaries. A major improvement made to the previous mathematical model is based on solute atoms conservation and diffusion theory. The capability and validity of the novel model is demonstrated by a binary alloy system. The simulation results are shown to quantitatively reproduce the essential features of particle coarsening near grain boundaries in certain alloys: a) precipitation Free Zones (PFZs) form near grain boundaries, b) the width of PFZs is proportional to square root of time, c) particles at the edge of PFZs are larger than those inside the grain. This novel model is shown to be well suited in describing particle coarsening near grain boundaries. On the other hand, it proves the credibility of the theories built in our mathematical model, i.e., the formation of PFZs near grain boundaries is caused by diffusion of solute atoms. / Thesis / Master of Applied Science (MASc)