Abstract: It is well known that chaos exists in systems of ordinary differential equations (ODEs), however, the study of chaos in partial differential equations (PDEs) remains rather new and unexplored. This is in part due to the computational resources needed to accurately simulate such systems. However, recent improvements of graphics processing units (GPUs) for use in general computing may provide a fast and economical way to solve complex systems such as PDEs. This talk will discuss the development of an algorithm which both numerically solves and determines the existence of chaos in nonlinear PDEs while utilizing the multiprocessor architecture of the GPU. This new method will aid in our search for simple examples of chaotic PDEs.