General order conditions for stochastic partitioned Runge-Kutta methods
For researchers in numerical analysis of stochastic differential equations, this provides a theoretical framework for analyzing and simplifying order conditions of SPRK methods.
The paper develops a general order theory for stochastic partitioned Runge-Kutta methods using stochastic B-series and multicolored trees, and applies it to prove the order of known methods while showing how to reduce order conditions, particularly for preserving quadratic invariants.
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.