Second-order stochastic leap-frog algorithm for langevin simulation.

Qiant, J. ; Habib, S.

Technical Information Center Oak Ridge Tennessee

关键词: Stochastic processes;    Langevin equation;    Algorithms;    Simulation;   

RP-ID  :  DE2001768728

学科分类：工程和技术（综合）

美国|英语

来源: National Technical Reports Library

【 摘 要 】

Langevin simulation provides an effective way to study collisional effects in beams by reducing the six-dimensional Fokker-Planck 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 leap-frog algorithm for the numerical integration of Langevin stochastic differential equations with multiplicative noise is proposed and tested. The algorithm has a second-order 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 mechanic oscillator with multiplicative noise.