Delay Equations Approximation And Application
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| Author | : MEINARDUS |
| Publisher | : Birkhäuser |
| Total Pages | : 351 |
| Release | : 2013-03-08 |
| Genre | : Science |
| ISBN | : 303487376X |
The international symposium held in October 1984 at the Uni versity of Mannheim was the first with the special aim to expose the connection of the Theory of Delay Eauations and Approximation Theory with the emphasis on constructive methods and applications. Although the separate character of both domains is reflected by their historical development, the latest research shows that the numerical treatment of Delay Equations leads to various appro ximation and optimization problems. An introductory survey of this circle of problems written by the editors is included at the beginning of the book. Delay Equations have their origin in domains of applications, such as physics, engineering, biology, medicine and economics. They appear in connection with the fundamental problem to analyse a retarded process from the real world, to develop a corresponding mathematical model and to determine the future behavior. Thirty mathematicians attended the conference coming from Germany, West- and Eastern Europe and the United States- more than twenty of them presented a research talk. The lectures about Delay Equations were mainly oriented on the following subjects: single-step, multi-step and spline methods; monotonicity methods for error estimations; asymptotic behavior 10 and periodicity of solutions. The topics of the talks on Approxi mation Theory covered different aspects of approximation by poly nomials, splines and rational functions and their numerical rea lization. Additionally included in the scientific program was a special session on Open Problems, where several suggestions were made for further research concerning both fields.
| Author | : Dimitri Breda |
| Publisher | : Springer |
| Total Pages | : 162 |
| Release | : 2014-10-21 |
| Genre | : Science |
| ISBN | : 149392107X |
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 implementing the proposed numerical methods. A number of proofs is given to furnish a solid foundation, but the emphasis is on the (unifying) idea of the pseudospectral technique for the stability analysis of DDEs. It is aimed at advanced students and researchers in applied mathematics, in dynamical systems and in various fields of science and engineering, concerned with delay systems. A relevant feature of the book is that it also provides the Matlab codes to encourage the readers to experience the practical aspects. They could use the codes to test the theory and to analyze the performances of the methods on the given examples. Moreover, they could easily modify them to tackle the numerical stability analysis of their own delay models.
| Author | : Patrick W Nelson |
| Publisher | : World Scientific |
| Total Pages | : 153 |
| Release | : 2010-06-25 |
| Genre | : Technology & Engineering |
| ISBN | : 9814464880 |
This book comprehensively presents a recently developed novel methodology for analysis and control of time-delay systems. Time-delays frequently occurs in engineering and science. Such time-delays can cause problems (e.g. instability) and limit the achievable performance of control systems. The concise and self-contained volume uses the Lambert W function to obtain solutions to time-delay systems represented by delay differential equations. Subsequently, the solutions are used to analyze essential system properties and to design controllers precisely and effectively.
| Author | : Tamás Insperger |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 181 |
| Release | : 2011-07-15 |
| Genre | : Mathematics |
| ISBN | : 1461403359 |
This book presents the recently introduced and already widely referred semi-discretization method for the stability analysis of delayed dynamical systems. Delay differential equations often come up in different fields of engineering, like feedback control systems, machine tool vibrations, balancing/stabilization with reflex delay. The behavior of such systems is often counter-intuitive and closed form analytical formulas can rarely be given even for the linear stability conditions. If parametric excitation is coupled with the delay effect, then the governing equation is a delay differential equation with time periodic coefficients, and the stability properties are even more intriguing. The semi-discretization method is a simple but efficient method that is based on the discretization with respect to the delayed term and the periodic coefficients only. The method can effectively be used to construct stability diagrams in the space of system parameters.
| Author | : Simo Särkkä |
| Publisher | : Cambridge University Press |
| Total Pages | : 327 |
| Release | : 2019-05-02 |
| Genre | : Business & Economics |
| ISBN | : 1316510085 |
With this hands-on introduction readers will learn what SDEs are all about and how they should use them in practice.
| Author | : Yang Kuang |
| Publisher | : Academic Press |
| Total Pages | : 413 |
| Release | : 1993-03-05 |
| Genre | : Mathematics |
| ISBN | : 0080960022 |
Delay Differential Equations emphasizes the global analysis of full nonlinear equations or systems. The book treats both autonomous and nonautonomous systems with various delays. Key topics addressed are the possible delay influence on the dynamics of the system, such as stability switching as time delay increases, the long time coexistence of populations, and the oscillatory aspects of the dynamics. The book also includes coverage of the interplay of spatial diffusion and time delays in some diffusive delay population models. The treatment presented in this monograph will be of great value in the study of various classes of DDEs and their multidisciplinary applications.
| Author | : Alfredo Bellen |
| Publisher | : OUP Oxford |
| Total Pages | : 410 |
| Release | : 2003-03-20 |
| Genre | : Mathematics |
| ISBN | : 0191523135 |
The main purpose of the book is to introduce the readers to the numerical integration of the Cauchy problem for delay differential equations (DDEs). Peculiarities and differences that DDEs exhibit with respect to ordinary differential equations are preliminarily outlined by numerous examples illustrating some unexpected, and often surprising, behaviours of the analytical and numerical solutions. The effect of various kinds of delays on the regularity of the solution is described and some essential existence and uniqueness results are reported. The book is centered on the use of Runge-Kutta methods continuously extended by polynomial interpolation, includes a brief review of the various approaches existing in the literature, and develops an exhaustive error and well-posedness analysis for the general classes of one-step and multistep methods. The book presents a comprehensive development of continuous extensions of Runge-Kutta methods which are of interest also in the numerical treatment of more general problems such as dense output, discontinuous equations, etc. Some deeper insight into convergence and superconvergence of continuous Runge-Kutta methods is carried out for DDEs with various kinds of delays. The stepsize control mechanism is also developed on a firm mathematical basis relying on the discrete and continuous local error estimates. Classical results and a unconventional analysis of "stability with respect to forcing term" is reviewed for ordinary differential equations in view of the subsequent numerical stability analysis. Moreover, an exhaustive description of stability domains for some test DDEs is carried out and the corresponding stability requirements for the numerical methods are assessed and investigated. Alternative approaches, based on suitable formulation of DDEs as partial differential equations and subsequent semidiscretization are briefly described and compared with the classical approach. A list of available codes is provided, and illustrative examples, pseudo-codes and numerical experiments are included throughout the book.
| Author | : Halanay |
| Publisher | : Academic Press |
| Total Pages | : 543 |
| Release | : 1966-01-01 |
| Genre | : Computers |
| ISBN | : 0080955290 |
| Author | : Walter A. Strauss |
| Publisher | : John Wiley & Sons |
| Total Pages | : 467 |
| Release | : 2007-12-21 |
| Genre | : Mathematics |
| ISBN | : 0470054565 |
Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them. It provides the student a broad perspective on the subject, illustrates the incredibly rich variety of phenomena encompassed by it, and imparts a working knowledge of the most important techniques of analysis of the solutions of the equations. In this book mathematical jargon is minimized. Our focus is on the three most classical PDEs: the wave, heat and Laplace equations. Advanced concepts are introduced frequently but with the least possible technicalities. The book is flexibly designed for juniors, seniors or beginning graduate students in science, engineering or mathematics.
| Author | : hal smith |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 178 |
| Release | : 2010-09-29 |
| Genre | : Mathematics |
| ISBN | : 1441976469 |
This book is intended to be an introduction to Delay Differential Equations for upper level undergraduates or beginning graduate mathematics students who have a reasonable background in ordinary differential equations and who would like to get to the applications quickly. The author has used preliminary notes in teaching such a course at Arizona State University over the past two years. This book focuses on the key tools necessary to understand the applications literature involving delay equations and to construct and analyze mathematical models involving delay differential equations. The book begins with a survey of mathematical models involving delay equations.
