Quadratized Taylor series methods for ODE numerical integration

Alessandro Borri, Francesco Carravetta and Pasquale Palumbo

Applied Mathematics and Computation, 2023, vol. 458, issue C

Abstract: 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).

Keywords: Ordinary differential equations; Taylor series methods; Exact quadratization; Systems immersion; Automatic differentiation (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:458:y:2023:i:c:s009630032300406x

DOI: 10.1016/j.amc.2023.128237

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