Stability and periodic solutions of ordinary and functional differential equations /
In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrang...
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Main Authors: | |
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Corporate Authors: | |
Published: |
Academic Press,
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Publisher Address: | Orlando : |
Publication Dates: | 1985. |
Literature type: | eBook |
Language: | English |
Series: |
Mathematics in science and engineering ;
v. 178 |
Subjects: | |
Online Access: |
http://www.sciencedirect.com/science/bookseries/00765392/178 |
Summary: |
In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank. |
Carrier Form: | 1 online resource (x, 337 pages) : illustrations. |
Bibliography: | Includes bibliographical references (pages 325-331). |
ISBN: |
9780080958675 0080958672 |
Index Number: | QA372 |
CLC: | O175 |
Contents: |
Front Cover; Stability and Periodic Solutions of Ordinary and Functional Differential Equations; Copyright Page; Contents; Preface; Chapter 0 An Overview; 0.1 Survey of Chapter 1; 0.2 Survey of Chapter 2; 0.3 Survey of Chapter 3; 0.4 Survey of Chapter 4; Chapter 1 Linear Differential and Integrodifferential Equations; 1.0 The General Setting; 1.1 Linear Ordinary Differential Equations; 1.2 Periodic Solutions of Linear Differential Equations; 1.3 Linear Volterra Equations; 1.4 Periodic Solutions of Convolution Equations; 1.5 Periodic Solutions of Nonconvolution Equations. 1.6 Stability and BoundednessChapter 2 History, Motivation, Examples; 2.1 Classical Second-Order Equations; 2.2 Problems with a Delay; 2.3 Biology, Economics, and Epidemics; 2.4 Sources of Models; Chapter 3 Fixed-Point Theory; 3.1 Compactnes in Metric Spaces; 3.2 Contraction Mappings; 3.3 Existence Theorems for Linear Equations; 3.4 Schauder's Fixed-Point Theorem; 3.5 Existence Theorems for Nonlinear Equations; Chapter 4 Limit Sets, Periodicity, and Stability; 4.1 Ordinary Differential Equations; 4.2 Equations with Bounded Delays; 4.3 Volterra Equations with Infinite Delay. 4.4 Stability of Systems with Unbounded DelaysReferences; Author Index; Subject Index. |