An Adaptive Algorithm for Rough Differential Equations

Understand

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.