Numerical investigation of solutions of Langevin equations

Abstract

Two recent pieces of analysis predicted certain limiting behaviours of Langevin equations. This thesis concerns the numerical investigation of the range of validity of these two analyses. In the low-friction limit it has been suggested that quasi-symplectic integrators could be appropriate to handle long time integration. Based on two examples, it is concluded that quasi-symplectic time-stepper are slightly more ecient than standard schemes. In the opposite context of high friction, the long time integration problem can be addressed by approximating the second order Langevin equation by a rst order Smoluchowski equation, and recent research has provided an analytic error estimator for this approximation. The numerical examples studied here verify the accuracy of this error estimator.