High Weak Order Solver

This post summarizes our new high weak order methods for the SciML ecosystem, as implemented within the Google Summer of Code 2020 project. After an introductory part highlighting the differences between the strong and the weak approximation for stochastic differential equations, we look into the convergence and performance properties of a few representative new methods in case of a non-commutative noise process.

First and foremost, I would like to thank my mentors Chris Rackauckas, Moritz Schauer, and Yingbo Ma for their willingness to supervise me in this Google Summer of Code project. Although we are still at the very beginning of the project, we already had plenty of very inspiring discussion.