  Several numerical schemes are proposed for the solution of Nonequilibrium
Langevin Dynamics (NELD), and the rate of convergence is analyzed. Due to the
special deforming boundary conditions used, care must be taken when using
standard stochastic integration schemes, and we demonstrate a loss of
convergence for a naive implementation. We then present several first and
second order schemes, in the sense of strong convergence.

Numerical Analysis