𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Numerical Methods for Parameter Estimation in Nonlinear Differential Algebraic Equations

✍ Scribed by Hans Georg Bock; Ekaterina Kostina; Johannes P. Schlöder

Publisher
John Wiley and Sons
Year
2007
Tongue
English
Weight
459 KB
Volume
30
Category
Article
ISSN
0936-7195

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

Nonlinear Differential Algebraic Equations (DAEs) are an important class of models for dynamic processes. To establish models that describe the process behavior in a quantitatvely correct way, often parameters in the model have to be determined from observations or measurements of the process.

This paper reviews numerical methods for parameter estimation in DAEs. In particular the so‐called boundary value problem approach and a versatile realisation, the multiple shooting method for parameter estimation, are discussed. Several applications are given to show the numerical performance and the wide applicability of the methods. A difficulty that occurs in practical applications is that the experiments performed to obtain measurements for parameter estimation are expensive, but nevertheless do not guarantee satisfactory parameter accuracy. The optimization of one or more dynamic experiments in order to maximize the accuracy of the results of a parameter estimation subject to cost and further technical inequality constraints leads to very complex non‐standard optimal control problems. Newly developed methods for design of optimal experiments for nonlinear processes are briefly discussed. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

📜 SIMILAR VOLUMES

Numerical methods for nonlinear first-or
Numerical methods for nonlinear first-order partial differential equations with deviated variables
✍ Anna Baranowska 📂 Article 📅 2006 🏛 John Wiley and Sons 🌐 English ⚖ 169 KB

In the article classical solutions of initial problems for nonlinear differential equations with deviated variables are approximated by solutions of quasilinear systems of difference equations. Interpolating operators on the Haar pyramid are used. Sufficient conditions for the convergence of the met

A seventh-order numerical method for sol
A seventh-order numerical method for solving boundary value nonlinear ordinary differential equations
✍ R. P. Tewarson 📂 Article 📅 1982 🏛 John Wiley and Sons 🌐 English ⚖ 261 KB

## Abstract A numerical method for solving two‐point boundary value problems associated with systems of first‐order nonlinear ordinary differential equations is described. It needs three function evaluations for each sub‐interval and is of order O(__h__^7^), where __h__ is the space chop. Results o

Variational Numerical Methods for Solvin
Variational Numerical Methods for Solving Nonlinear Diffusion Equations Arising in Image Processing
✍ Angela Handlovičová; Karol Mikula; Fiorella Sgallari 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 264 KB

In this paper we give a general, robust, and efficient approach for numerical solutions of partial differential equations (PDEs) arising in image processing and computer vision. The well-established variational computational techniques, namely, finite element, finite volume, and complementary volume