An Adaptive Algorithm for Rough Differential Equations

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.