Articolo in rivista, 2023, ENG, 10.1016/j.amc.2023.128237

Quadratized Taylor series methods for ODE numerical integration

Alessandro Borri and Francesco Carravetta and Pasquale Palumbo

Institute of Systems analysis and Computer Science (IASI), National Research Council (CNR), Via dei Taurini 19, 00185, Roma, Italy; Department of Biotechnology and Biosciences (BtBs), University of Milano-Bicocca, Piazza della Scienza 2, U3 building, room 4024, 20126 Milan, Italy

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).

Applied mathematics and computation 458

Keywords

Ordinary differential equations, Taylor series methods, Exact quadratization, Systems immersion, Automatic differentiation

CNR authors

Palumbo Pasquale, Carravetta Francesco, Borri Alessandro

CNR institutes

IASI – Istituto di analisi dei sistemi ed informatica "Antonio Ruberti"