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 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.