Steady-state density preserving method for stochastic mechanical systems

• Published in: European physical journal plus Vol. 136; no. 8; p. 799
• Main Author: de la Cruz, H.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01-08-2021; Springer Nature B.V
• Subjects: Applied and Technical Physics; Approximation; Atomic; Complex Systems; Condensed Matter Physics; Focus Point on Uncertainty Quantification of Modelling and Simulation in Physics and Related Areas: From Theoretical to Computational Techniques; Mathematical and Computational Physics; Mathematical functions; Mechanical systems; Methods; Molecular; Nonlinear systems; Numerical analysis; Numerical methods; Optical and Plasma Physics; Physics; Physics and Astronomy; Probability density functions; Regular Article; Steady state; Theoretical
• ISSN: 2190-5444; 2190-5444
• DOI: 10.1140/epjp/s13360-021-01770-9

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.