General order conditions for stochastic partitioned Runge-Kutta methods
Numerical Analysis
2019-07-19 v2
Abstract
In this paper stochastic partitioned Runge-Kutta (SPRK) methods are considered. A general order theory for SPRK methods based on stochastic B-series and multicolored, multishaped rooted trees is developed. The theory is applied to prove the order of some known methods, and it is shown how the number of order conditions can be reduced in some special cases, especially that the conditions for preserving quadratic invariants can be used as simplifying assumptions.
Keywords
Cite
@article{arxiv.1703.02067,
title = {General order conditions for stochastic partitioned Runge-Kutta methods},
author = {Sverre Anmarkrud and Kristian Debrabant and Anne Kværnø},
journal= {arXiv preprint arXiv:1703.02067},
year = {2019}
}