Testing the method of multiple scales and the averaging principle for model parameter estimation of quasiperiodic two time-scale models

Papáček, Štěpán, and Matonoha, Ctirad. "Testing the method of multiple scales and the averaging principle for model parameter estimation of quasiperiodic two time-scale models." Programs and Algorithms of Numerical Mathematics. Prague: Institute of Mathematics CAS, 2023. 163-172. <http://eudml.org/doc/299006>.

@inProceedings{Papáček2023,
abstract = {Some dynamical systems are characterized by more than one time-scale, e.g. two well separated time-scales are typical for quasiperiodic systems. The aim of this paper is to show how singular perturbation methods based on the slow-fast decomposition can serve for an enhanced parameter estimation when the slowly changing features are rigorously treated. Although the ultimate goal is to reduce the standard error for the estimated parameters, here we test two methods for numerical approximations of the solution of associated forward problem: (i) the multiple time-scales method, and (ii) the method of averaging. On a case study, being an under-damped harmonic oscillator containing two state variables and two parameters, the method of averaging gives well (theoretically predicted) results, while the use of multiple time-scales method is not suitable for our purposes.},
author = {Papáček, Štěpán, Matonoha, Ctirad},
booktitle = {Programs and Algorithms of Numerical Mathematics},
keywords = {dynamical system; singular perturbation; averaging; parameter estimation; slow-fast decomposition; damped oscillations},
location = {Prague},
pages = {163-172},
publisher = {Institute of Mathematics CAS},
title = {Testing the method of multiple scales and the averaging principle for model parameter estimation of quasiperiodic two time-scale models},
url = {http://eudml.org/doc/299006},
year = {2023},
}

TY - CLSWK
AU - Papáček, Štěpán
AU - Matonoha, Ctirad
TI - Testing the method of multiple scales and the averaging principle for model parameter estimation of quasiperiodic two time-scale models
T2 - Programs and Algorithms of Numerical Mathematics
PY - 2023
CY - Prague
PB - Institute of Mathematics CAS
SP - 163
EP - 172
AB - Some dynamical systems are characterized by more than one time-scale, e.g. two well separated time-scales are typical for quasiperiodic systems. The aim of this paper is to show how singular perturbation methods based on the slow-fast decomposition can serve for an enhanced parameter estimation when the slowly changing features are rigorously treated. Although the ultimate goal is to reduce the standard error for the estimated parameters, here we test two methods for numerical approximations of the solution of associated forward problem: (i) the multiple time-scales method, and (ii) the method of averaging. On a case study, being an under-damped harmonic oscillator containing two state variables and two parameters, the method of averaging gives well (theoretically predicted) results, while the use of multiple time-scales method is not suitable for our purposes.
KW - dynamical system; singular perturbation; averaging; parameter estimation; slow-fast decomposition; damped oscillations
UR - http://eudml.org/doc/299006
ER -