Parameter estimation by quasilinearization in  differential equations with state-dependent delays

Ferenc Hartung

doi:10.3934/dcdsb.2013.18.1611

Article Contents

2013, Volume 18, Issue 6: 1611-1631. Doi: 10.3934/dcdsb.2013.18.1611

This issue Previous Article Singular limit of viscous Cahn-Hilliard equations with memory and dynamic boundary conditions Next Article A state-dependent delay equation with negative feedback and "mildly unstable" rapidly oscillating periodic solutions

Parameter estimation by quasilinearization in differential equations with state-dependent delays

Ferenc Hartung^1,

1.
Department of Mathematics and Computing, University of Pannonia, H-8201 Veszprém, P.O.Box 158

Received: January 2012

Revised: February 2012

Published: August 2013

Abstract / Introduction Related Papers Cited by

Abstract

In this paper we study a parameter estimation method in functional differential equations with state-dependent delays using a quasilinearization technique. We define the method, prove its convergence under certain conditions, and test its applicability in numerical examples. We estimate infinite dimensional parameters such as coefficient functions, delay functions and initial functions in state-dependent delay equations. The method uses the derivative of the solution with respect to the parameters. The proof of the convergence is based on the Lipschitz continuity of the derivative with respect to the parameters.

Keywords:

Parameter estimation,
delay differential equation,
state-dependent delay,
quasilinearization,
differentiability with respect to parameters.

Mathematics Subject Classification: Primary: 34K05; Secondary: 93B30.

Citation:

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