Second-order stochastic leapfrog algorithm for multiplicative noise Brownian motion
- 1 November 2000
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review E
- Vol. 62 (5), 7430-7437
- https://doi.org/10.1103/physreve.62.7430
Abstract
A stochastic leapfrog algorithm for the numerical integration of Brownian motion 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. The noise may be white or colored. We apply the algorithm to a study of the approach towards equilibrium of an oscillator coupled nonlinearly to a heat bath and investigate the effect of the multiplicative noise (arising from the nonlinear coupling) on the relaxation time. This allows us to test the regime of validity of the energy-envelope approximation method.Keywords
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This publication has 21 references indexed in Scilit:
- Disordering Effects of Color in Nonequilibrium Phase Transitions Induced by Multiplicative NoisePhysical Review Letters, 1997
- Effects of multiplicative noise on fluctuation-induced transportPhysics Letters A, 1996
- Stochastic transient of a noisy van der Pol oscillatorPhysica A: Statistical Mechanics and its Applications, 1995
- Linear Stability Analysis for Bifurcations in Spatially Extended Systems with Fluctuating Control ParameterPhysical Review Letters, 1994
- Multiplicative Noise: Applications in Cosmology and Field TheoryAnnals of the New York Academy of Sciences, 1993
- Noise-induced relaxation of a quantum oscillator interacting with a thermal bathPhysics Letters A, 1993
- Nonlinear noise in cosmologyPhysical Review D, 1992
- Multiplicative noise effects on relaxations from marginal statesPhysical Review A, 1991
- Dissipative contributions of internal multiplicative noisePhysica A: Statistical Mechanics and its Applications, 1981
- Nonlinear generalized Langevin equationsJournal of Statistical Physics, 1973