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Quadratized Taylor series methods for ODE numerical integration
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DOI：10.1016/j.amc.2023.128237.png)
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摘要
En 中文
We focus on Taylor Series Methods (TSM) and Automatic Differentiation (AD) for the numerical solution of Ordinary Differential Equations (ODE) characterized by a vector field given by a finite composition of elementary and standard functions. We show that computational advantages are achieved if a kind of pre-processing said Exact Quadratization (EQ) is applied to the ODE before applying the TSM and the AD. In particular, when the ODE function is given by a formal polynomial (i.e. with real powers) of n variables and m monomials, the computational complexity required by our EQ based method for the calculation of the k-th order Taylor coefficient is O(k) whereas by using the existing AD methods it amounts to O(k2).
Keyword:
Ordinary differential equations
Taylor series methods
Exact quadratization
Systems immersion
Automatic differentiation
期刊
IF:
3.4
论文数:
2.3W
被引数:
3.3W
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