Operator analysis of the Langevin algorithm

By studying the Fokker-Planck equation in its operator form, various Langevin algorithms can be systematically derived and analyzed without the use of stochastic differential equations or the Kramers-Moyal expansion. New, but in a way canonical, second order Langevin algorithms are presented. The convergence behaviors of these new algorithms are numerically shown to be superior to that of the usual Runge-Kutta algorithm. (orig.)