English

An Adaptive Algorithm for Rough Differential Equations

Numerical Analysis 2023-07-25 v1 Numerical Analysis

Abstract

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.

Keywords

Cite

@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}
}