A Second Order Stochastic LeapFrog Algorithm for Langevin Simulation
Abstract
Langevin simulation provides an effective way to study collisional effects in beams by reducing the sixdimensional FokkerPlanck equation to a group of stochastic ordinary differential equations. These resulting equations usually have multiplicative noise since the diffusion coefficients in these equations are functions of position and time. Conventional algorithms, e.g. Euler and Heun, give only first order convergence of moments in a finite time interval. In this paper, a stochastic leapfrog algorithm for the numerical integration of Langevin stochastic differential equations with multiplicative noise is proposed and tested. The algorithm has a secondorder convergence of moments in a finite time interval and requires the sampling of only one uniformly distributed random variable per time step. As an example, we apply the new algorithm to the study of a mechanical oscillator with multiplicative noise.
 Publication:

Linac 2000
 Pub Date:
 2000
 DOI:
 10.48550/arXiv.physics/0008196
 arXiv:
 arXiv:physics/0008196
 Bibcode:
 2000lina.conf...89Q
 Keywords:

 Accelerator Physics
 EPrint:
 3 pages, 4 figures, to submit to XX International LINAC conference