Screen LibraryTheory of difference equations : numerical methods and applications /
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: | |
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| Published: |
Academic Press,
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| Publisher Address: | Boston : |
| Publication Dates: | 1988. |
| Literature type: | eBook |
| Language: | English |
| Series: |
Mathematics in science and engineering ;
v. 181 |
| Subjects: | |
| Online Access: |
http://www.sciencedirect.com/science/bookseries/00765392/181 |
| 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, 242 pages). |
| Bibliography: | Includes bibliographical references (pages 231-237) and index. |
| ISBN: |
9780080958699 0080958699 |
| Index Number: | QA431 |
| CLC: | O175 |
| Contents: |
Front Cover; Theory of Difference Equations: Numerical Methods and Applications; Copyright Page; Contents; Preface; CHAPTER 1 Preliminaries; 1.0. Introduction; 1.1. Operators? and E; 1.2. Negative Powers of?; 1.3. Factorial Powers and Discrete Taylor Formulas; 1.4. Bernoulli Numbers and Polynomials; 1.5. Difference Equations; 1.6. Comparison Results; 1.7. Problems; 1.8. Notes; CHAPTER 2 Linear Difference Equations; 2.0. Introduction; 2.1. Fundamental Theory; 2.2. The Method of Variation of Constants; 2.3. Equations with Constant Coefficients; 2.4. Use of Operators? and E. 2.5. Method of Generating Functions2.6. Stability of Solutions; 2.7. Absolute Stability; 2.8. Boundary Value Problems for Second Order Equations; 2.9. Problems; 2.10. Notes; CHAPTER 3 Linear Systems of Difference Equations; 3.0. Introduction; 3.1. Basic Theory; 3.2. Method of Variation of Constants; 3.3. Systems Representing Higher Order Equations; 3.4. Periodic Solutions; 3.5. Boundary Value Problems; 3.6. Problems; 3.7. Notes; CHAPTER 4 Stability Theory; 4.0. Introduction; 4.1. Stability Notions; 4.2. The Linear Case; 4.3. Autonomous Linear Systems. 4.4. Linear Equations with Periodic Coefficients4.5. Use of the Comparison Principle; 4.6. Variation of Constants; 4.7. Stability by First Approximation; 4.8. Lyapunov Functions; 4.9. Domain of Asymptotic Stability; 4.10. Converse Theorems; 4.11. Total and Practical Stabilities; 4.12. Problems; 4.13. Notes; CHAPTER 5 Applications to Numerical Analysis; 5.0. Introduction; 5.1. Iterative Methods; 5.2. Local Results; 5.3. Semilocal Results; 5.4. Unstable Problems: Miller's, Olver's and Clenshaw's Algorithms; 5.5. Unstable Problems: the ""SWEEP"" Method; 5.6. Monotone Iterative Methods. 5.7. Monotone Iterative Methods (Continued)5.8. Problems; 5.9. Notes; CHAPTER 6 Numerical Methods for Differential Equations; 6.0. Introduction; 6.1. Linear Multistep Methods; 6.2. Finite Interval; 6.3. Infinite Interval; 6.4. Nonlinear Case; 6.5. Other Techniques; 6.6. The Method of Lines; 6.7. Spectrum of a Family of Matrices; 6.8. Problems; 6.9. Notes; CHAPTER 7 Models of Real World Phenomena; 7.0. Introduction; 7.1. Linear Models for Population Dynamics; 7.2. The Logistic Equation; 7.3. Distillation of a Binary Liquid; 7.4. Models from Economics; 7.5. Models of Traffic in Channels. 7.6. Problems7.7. Notes; Appendix A; A1. Function of Matrices; A2. Properties of the Component Matrices and and Sequences of Matrices; A3. Integral Form of a Function of Matrix; A.4. Jordan Canonical Form; A.5. Norms of Matrices and Related Topics; A.6. Nonnegative Matrices; Appendix B-The Schur Criterium; Appendix C-Chebyshev Polynomials; C.l. Definitions; C.2. Properties of Tn(z) and Un(z); Solutions to the Problems; References; Index; Mathematics in Science and Engineering. |