Conservative methods for stochastic differential equations with a conserved quantity
Numerical Analysis
2014-11-10 v1
Abstract
This paper proposes a novel conservative method for numerical computation of general stochastic differential equations in the Stratonovich sense with a conserved quantity. We show that the mean-square order of the method is if noises are commutative and that the weak order is also . Since the proposed method may need the computation of a deterministic integral, we analyse the effect of the use of quadrature formulas on the convergence orders. Furthermore, based on the splitting technique of stochastic vector fields, we construct conservative composition methods with similar orders as the above method. Finally, numerical experiments are presented to support our theoretical results.
Cite
@article{arxiv.1411.1819,
title = {Conservative methods for stochastic differential equations with a conserved quantity},
author = {Chuchu Chen and David Cohen and Jialin Hong},
journal= {arXiv preprint arXiv:1411.1819},
year = {2014}
}