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arXiv · 2307.12590

An Adaptive Algorithm for Rough Differential Equations

Christian Bayer·Simon Breneis·Terry Lyons
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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.

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Christian Bayer, Simon Breneis, Terry Lyons. 2023-07-24. An Adaptive Algorithm for Rough Differential Equations. https://arxiv.org/abs/2307.12590

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