We present an adaptive algorithm for effectively solving rough differential equations (RDEs) using the log-ODE method. The algorithm is based on an error representation formula that accurately describes the contribution of local errors to the global error. By incorporating a cost model, our algorithm efficiently determines whether to refine the time grid or increase the order of the log-ODE method. In addition, we provide several examples that demonstrate the effectiveness of our adaptive algorithm in solving RDEs.
@article{arxiv.2307.12590,
title = {An Adaptive Algorithm for Rough Differential Equations},
author = {Christian Bayer and Simon Breneis and Terry Lyons},
journal= {arXiv preprint arXiv:2307.12590},
year = {2023}
}