Stability of linear delay differential equations : a numerical approach with MATLAB /: a numerical approach with MATLAB. ([2014])

• Record Type: Book
• Further Information: Note: Dimitri Breda, Stefano Maset, Rossana Vermiglio.
• Authors: Breda, Dimitri; Maset, Stefano; Vermiglio, Rossana
• 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.
• Publisher Details: New York, NY : Springer
• Publication Date: 2014
• Copyright Date: 2015
• Extent: 1 online resource (xi, 158 pages), illustrations (some color)
• Subjects: 515/.354; Mathematics; Differential equations, Linear -- Numerical solutions; Delay differential equations -- Numerical solutions; Systems theory; Numerical analysis; MATHEMATICS -- Calculus; MATHEMATICS -- Mathematical Analysis; Delay differential equations -- Numerical solutions; Differential equations, Linear -- Numerical solutions; Mathematics -- Number Systems; Technology & Engineering -- Automation; Numerical analysis; Automatic control engineering; Science -- System Theory; Cybernetics & systems theory; Electronic books
• Languages: English
• ISBNs: 9781493921072; 1493921061; 9781493921065
• Related ISBNs: 149392107X; 9781493921065
• Notes: Note: Includes bibliographical references.; Note: Online resource; title from PDF title page (SpringerLink, viewed November 10, 2014).
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.