A fourth-order numerical integrator for stochastic Langevin equations

Stochastic differential equations (SDE’s) can be numerically integrated using second-order accuracy methods. Higher order schemes are not in use because of the complexity of the algorithm and because of the difficulties in producing non-Gaussian noises. Yet for the case of the Langevin equation (LE) which is a subclass of SDE’s, high order integrators can be developed. A fast fourth-order integrator is presented here. The improved efficiency of the new integrator allows for solution of systems which could not be integrated accurately with the standard second-order methods.