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.

翻译：我们提出了一种利用log-ODE方法有效求解粗糙微分方程的自适应算法。该算法基于一个误差表示公式，该公式精确描述了局部误差对全局误差的贡献。通过引入成本模型，我们的算法能够高效地决定是细化时间网格还是提高log-ODE方法的阶数。此外，我们提供了若干算例，以展示该自适应算法在求解粗糙微分方程中的有效性。