Solving Langevin equation with the bicolour rooted tree method

Jiabin You and Hong Zhao

Physica A: Statistical Mechanics and its Applications, 2010, vol. 389, issue 18, 3769-3778

Abstract: Stochastic differential equations, especially the one called Langevin equation, play an important role in many fields of modern science. In this paper, we use the bicolour rooted tree method, which is based on the stochastic Taylor expansion, to get the systematic pattern of the high order algorithm for Langevin equation. We propose a popular test problem, which is related to the energy relaxation in the double well, to test the validity of our algorithm and compare our algorithm with other usually used algorithms in simulations. And we also consider the time-dependent Langevin equation with the Ornstein–Uhlenbeck noise as our second example to demonstrate the versatility of our method.

Keywords: Stochastic processes; Langevin equation; Numerical simulation (search for similar items in EconPapers)
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:389:y:2010:i:18:p:3769-3778

DOI: 10.1016/j.physa.2010.05.040

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