A method for solving the parameter identification problem for ordinary differential equations of the second order
type: Item
instance of: scholarly article
title: A method for solving the parameter identification problem for ordinary differential equations of the second order
zbMATH Open document ID: 0854.65070
DOI: 10.1016/0096-3003(95)00098-4
author: Rudolf Scitovski
author: Dragan Jukić
published in: Applied Mathematics and Computation
publication date: 1996-09-08T00:00:00Z
review text: This paper deals with the determination of optimal values for some unknown parameters \(p = (p_1,\dots,p_s)\) entering in a second-order differential equation \(y'' = f(t,y,y',p)\) from a (large) set of experimental data \((t_i, y_i)\) of some solution. Here the optimality of \(p\) must be understood in the sense to minimize the differences between the experimental values and the values given by the differential equation. The above problem falls within the class of parameter identification problems for which several approaches have been proposed. Here the authors combine the ideas of several previous approaches in order to determine its optimal solution. Firstly, they determine a smooth function from the given experimental data by using the so-called moving least squares techniques. Then, they discretize the differential equation by means of the trapezoidal rule and solve (in the least squares sense) the resulting set of algebraic equations in the parameters. Finally, further refinement of the parameters are proposed. To test the efficiency of the method, the authors apply it to a second-order equation which arises in the modelization of an enzyme effusion problem (\textit{Hemker} \& \textit{Kok}, T.R. NM-R9301, Mathematisch Centrum, Amsterdam) which contains four parameters and to a linear second-order equation with two parameters.
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 34A55
Mathematics Subject Classification ID: 65L60
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 892426
zbMATH Keywords: inverse problem
zbMATH Keywords: second-order differential equation
zbMATH Keywords: experimental data
zbMATH Keywords: parameter identification problems
zbMATH Keywords: moving least squares
reviewed by: Manuel Calvo
MaRDI profile type: Publication
full work available at URL: 0096-3003(95)00098-4
OpenAlex ID: W1996076939
cites work: Q4092892
cites work: A Spline Least Squares Method for Numerical Parameter Estimation in Differential Equations
cites work: The Differentiation of Pseudo-Inverses and Nonlinear Least Squares Problems Whose Variables Separate
cites work: Algorithms for Separable Nonlinear Least Squares Problems
cites work: Q4031275
cites work: Short Lecture Session
cites work: Q4114633
cites work: Q3664353
cites work: Parameter identification for an abstract Cauchy problem by quasilinearization
cites work: Moving least squares interpolation with thin-plate splines and radial basis functions
cites work: Q3210792
cites work: Q3978923
cites work: Discussion of parameter estimation in biological modelling: Algorithms for estimation and evaluation of the estimates
cites work: Q3042314
cites work: Q4724224
cites work: Q3996878
cites work: Q4724230
cites work: Multivariate interpolation of arbitrarily spaced data by moving least squares methods
cites work: Rate of Convergence of Shepard's Global Interpolation Formula
cites work: Surfaces Generated by Moving Least Squares Methods
cites work: Q3795136
cites work: Q4692387
cites work: Q3359644
cites work: Q4739659
cites work: Q3702408
cites work: Q5652137
cites work: The automatic integration of ordinary differential equations
description: scientific article; zbMATH DE number 892426