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DY: Fachverband Dynamik und Statistische Physik

DY 27: Poster: Nonlinear Dynamics, Pattern Formation, Granular Matter

DY 27.4: Poster

Mittwoch, 19. März 2025, 15:00–18:00, P4

Numerical Differentiation by Integrated Series Expansion (NDBISE) in the Context of Ordinary Differential Equation Estimation Problems — •Oliver Strebel — Angelstr. 17, D-75392 Deckenpfronn

Parameter or model estimation of ordinary differential equations (ODE) involves nowadays frequently the numerical calculation of derivatives from noisy data. This article presents a novel differentiation method (NDBISE) for such calculations. The method is benchmarked against 57 differential equations and compared to other numerical differentiation methods. The hyperparameters of all these methods are optimized in order to get a reasonable comparison. The resilience against larger noise or fewer data points per time interval is examined. It turns out that the novel method is overall superior to the other methods.

The derivative for the 42 real world data points of the Hudson bay lynx hare data (years 1900-1920) is also calculated. The results match the derivative of a curve fit to the data points astonishingly close. Using a Savitsky-Golay filter the method can be leveraged to calculate second and third order derivatives, so that the results are close to the theoretically expected outcome.

Preprint: https://doi.org/10.21203/rs.3.rs-5465961/v1

Keywords: ordinary differential equation; model estimation; parameter estimation; time series analysis; system identification