The aim of the project is to investigate methods for the numerical solution of the classical N-body problem on graphics processing units. In particular celestial mechanics and molecular dynamics simulations will be performed. One goal of the research is to implement a tree code in CUDA for the solution of long range potential problems (gravity). The implementation of a number of sophisticated integrators for the equations of motion in CUDA will also be attempted. Among these are the Force Gradient class of integrators and the Variational integrators.