Authors: Ferenc A. Bartha, Hans Z. Munthe-Kaas

Journal: Discrete and Continuous Dynamical Systems - Ser. A, (2014) 34:903 - 914

Abstract: We present an algorithm based on Automatic Differentiation for computing general B-series of vector fields. The algorithm has a computational complexity depending linearly on n, and provides a practical way of computing B-series up to a moderately high order d. Compared to Automatic Differentiation for computing Taylor series solutions of differential equations, the proposed algorithm is more general, since it can compute any B-series. However the computational cost of the proposed algorithm grows much faster in d than a Taylor series method, thus very high order B-series are not tractable by this approach.

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