Carcinus maenas (The European Green Crab) have been introduced to the east and west coasts of North America. The crab population has spread to become an established invasive species and impacted resident species by causing severe economic and ecological damage. This talk presents two integro-difference models; one for the spread of the crab and one to model the control of the crab by introducing Sacculina carcini. Under certain conditions, the parasite has been shown to be an effective biological control agent.
Anderson Acceleration (AA) Method is a type of iterative algorithm used to estimate the solutions through a system of linear equations. Generally, it accel- erates the convergence of the fixed point problem. However, there has not much development in using AA algorithm in fluid applications in general and the Stokes problem in particular. The goal is to solve for the velocity field and the pressure profile of the Stokes equations using AA as a solver. Furthermore, we will compare the number of iterations, the computational time, the error estimation between AA method and the standard GMRES through some test problems. The Stokes equations will be discretized using finite element method (FEM). This can be written in the terms of the saddle point problem in which the Uzawa algorithm is executed to lead to the application of AA method.