WIAS Preprint No. 3013, (2023)

An adaptive algorithm for rough differential equations


Authors

  • Bayer, Christian
    ORCID: 0000-0002-9116-0039
  • Breneis, Simon
  • Lyons, Terry

2020 Mathematics Subject Classification

  • 60L20 65C30 65L50

Keywords

  • Rough differential equations, log-ODE method, adaptive mesh refinement, a-posteriori error estimation

DOI

10.20347/WIAS.PREPRINT.3013

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 deter- mines 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 adapctive algorithm in solving RDEs.

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