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Stability of linear delay differential equations : a numerical approach with MATLAB

Author: Dimitri Breda; Stefano Maset; Rossana Vermiglio
Publisher: New York, NY : Springer, [2014] ©2015
Series: SpringerBriefs in electrical and computer engineering., Control, automation and robotics.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
This book presents the authors' recent work on the numerical methods for the stability analysis of linear autonomous and periodic delay differential equations, which consist in applying pseudospectral techniques to discretize either the solution operator or the infinitesimal generator and in using the eigenvalues of the resulting matrices to approximate the exact spectra. The purpose of the book is to provide a  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Breda, Dimitri.
Stability of Linear Delay Differential Equations : A Numerical Approach with MATLAB.
New York, NY : Springer New York, ©2014
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Dimitri Breda; Stefano Maset; Rossana Vermiglio
ISBN: 9781493921072 149392107X 1493921061 9781493921065
OCLC Number: 894508863
Description: 1 online resource (xi, 158 pages) : illustrations (some color).
Contents: Preface; Contents; 1 Introduction; 1.1 Linear Ordinary Differential Equations; 1.2 Simple Linear Delay Differential Equations; 1.3 An Example from Population Dynamics; 1.4 An Example from Mechanical Engineering; 1.5 Scopes and Synopsis; Part ITheory; 2 Notation and Basics; 2.1 Notation; 2.2 The Cauchy Problem; 2.3 Stability of Solutions; 3 Stability of Linear Autonomous Equations; 3.1 The Solution Operator Semigroup and the Infinitesimal Generator; 3.2 Spectral Properties and the Characteristic Equation; 3.3 Linearization and Equilibria; 4 Stability of Linear Periodic Equations. 4.1 The Evolution Operator and the Monodromy Operator4.2 Linearization and Periodic Solutions; Part IINumerical Analysis; 5 The Infinitesimal Generator Approach; 5.1 The Pseudospectral Differentiation Method; 5.2 The Piecewise Pseudospectral Differentiation Method; 5.3 Convergence Analysis; 5.3.1 A Related Collocation Problem; 5.3.2 Convergence of the Eigenvalues; 5.3.3 Quadrature for Distributed Delays; 5.4 Convergence of the Piecewise Method; 5.5 Other Methods; 6 The Solution Operator Approach; 6.1 The Pseudospectral Collocation Method; 6.1.1 Discretization of X; 6.1.2 Discretization of X+ 6.1.3 Discretization of T6.2 The Collocation Equation; 6.3 Convergence Analysis; 6.3.1 Convergence of the Eigenvalues of T""0362TN; 6.3.2 Convergence of the Eigenvalues of T""0362TM, N; 6.3.3 Quadrature for Distributed Delays; 6.4 Other Methods; Part IIIImplementation and Applications; 7 MATLAB Implementation; 7.1 Introducing the Model in MATLAB; 7.2 The Infinitesimal Generator Approach; 7.2.1 A Single Discrete Delay; 7.2.2 A Single Distributed Delay; 7.2.3 The Piecewise Method; 7.3 The Solution Operator Approach; 7.3.1 The Meshes; 7.3.2 The Matrix TM(1); 7.3.3 The Matrix TM, N(2). 7.3.4 The Matrix UM, N(1)7.3.5 The Matrix UN(2); 8 Applications; 8.1 Test Cases; 8.1.1 Test 1: Linear Autonomous Equations with a Discrete Delay; 8.1.2 Test 2: Linear Autonomous Equations with Multiple Discrete Delays; 8.1.3 Test 3: Linear Autonomous Equations with a Distributed Delay; 8.1.4 Test 4: Linear Autonomous Systems; 8.1.5 Test 5: Linear Periodic Equations; 8.1.6 Test 6: Linearized Periodic Equations; 8.2 Equilibria in Population Dynamics; 8.3 Periodic Problems in Engineering; References; Series Editors' Biographies.
Series Title: SpringerBriefs in electrical and computer engineering., Control, automation and robotics.
Responsibility: Dimitri Breda, Stefano Maset, Rossana Vermiglio.

Abstract:

This book presents the authors' recent work on the numerical methods for the stability analysis of linear autonomous and periodic delay differential equations, which consist in applying pseudospectral techniques to discretize either the solution operator or the infinitesimal generator and in using the eigenvalues of the resulting matrices to approximate the exact spectra. The purpose of the book is to provide a complete and self-contained treatment, which includes the basic underlying mathematics and numerics, examples from population dynamics and engineering applications, and Matlab programs.

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