Computing of B-series by automatic differentiation
Ferenc A. Bartha, Hans Munthe–Kaas
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We present an algorithm based on Automatic Differentiation for computing general B-series of vector fields $f\colon \mathbb{R}^n\rightarrow \mathbb{R}^n$. 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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We present an algorithm based on Automatic Differentiation for computing general B-series of vector fields $f\colon \mathbb{R}^n\rightarrow \mathbb{R}^n$.
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6
Citations
22
References
Tasks
Taylor series, Series (stratigraphy), Automatic differentiation, Computer science, Order (exchange), Numerical Analysis, Physical Sciences
Methods
Algorithm
Domains
Mathematics
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