In this work, we study two numerical strategies for solving a coupled system of distinct nonlinear partial differential equations, which can be used to model dual-lithology sedimentation. Using high-resolution bathymetry data of Lake Okeechobee, Florida, we study the stability and computational speed of these numerical strategies. The fully-explicit scheme is straightforward to implement and requires a relatively small amount of computation per time step. However, this simple numerical strategy has to use small time steps to ensure stability. These small time steps may render the explicit solver impractical for long-term and high-resolution basin simulations. As a comparison, we have implemented a semi-implicit scheme, where the two partial differential equations at each time step are solved implicitly in sequence. This semi-implicit scheme is numerically stable even for very large time steps. Using parallel computing, we have applied both schemes to a realistic case, Lake Okeechobee, Florida. The simulation successfully diffused material along a river-channel and into the lake. Both MPI-based implementations demonstrated satisfactory parallel efficiency on a multicore-based cluster.