Polymers are ubiquitous in a wide range of commercial products and applications. Polymers are melted to a liquid state, and are processed under precise conditions; giving rise to their unique properties. It is difficult to predict the ultimate properties of a polymeric fluid while it is interacting with a processing flow. In terms of mathematics, modeling polymeric solutions using stochastic differential equations to predict the configuration fields of the molecules is an appealing method to calculate the stress of the polymer fluid. This work employs the Finite Extensible Nonlinear Elastic (FENE) model for a polymeric molecule to limit the extent to which polymeric molecules can be elongated. The FENE model will be solved numerically by the stochastic differential equation approach. We implement a technique known as Brownian Configuration fields to simulate the configuration fields

of the springs. Results gained from the project will help predict the rheological behavior of a polymeric fluid under a given flow.