Abstract :
[en] Nonlinear (systems of) ordinary differential equations (ODEs) are common tools in the analysis of
complex one-dimensional dynamic systems.We propose a smoothing approach regularized by a quasilinearized
ODE-based penalty. Within the quasilinearized spline-based framework, the estimation
reduces to a conditionally linear problem for the optimization of the spline coefficients. Furthermore,
standard ODE compliance parameter(s) selection criteria are applicable.We evaluate the performances
of the proposed strategy through simulated and real data examples. Simulation studies suggest that the
proposed procedure ensures more accurate estimates than standard nonlinear least squares approaches
when the state (initial and/or boundary) conditions are not known.
Disciplines :
Physical, chemical, mathematical & earth Sciences: Multidisciplinary, general & others
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