Eur. Phys. J. Plus (2021) 136: 799
https://doi.org/10.1140/epjp/s13360-021-01770-9

Regular Article

Steady-state density preserving method for stochastic mechanical systems

School of Applied Mathematics, Fundação Getulio Vargas, Rio de Janeiro, Brazil

^a hugo.delacruz@fgv.br

Received: 18 May 2021
Accepted: 18 July 2021
Published online: 3 August 2021

Abstract

We devise a numerical method for the long-term integration of a class of damped second order stochastic mechanical systems. The introduced numerical scheme has the advantage of being completely explicit for general nonlinear systems, while in contrast with other commonly used integrators, it has the ability to compute the evolution of the system with high stability and precision in very large time intervals. Notably, the method has the important property of preserving for all values of the step size, the steady-state probability density function of any linear system with stationary solution. Several numerical experiments are presented to show the practical performance of the introduced method.