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| Author | : Uri M. Ascher |
| Publisher | : SIAM |
| Total Pages | : 304 |
| Release | : 1998-08-01 |
| Genre | : Mathematics |
| ISBN | : 0898714125 |
This book contains all the material necessary for a course on the numerical solution of differential equations.
| Author | : Fathalla A. Rihan |
| Publisher | : Springer Nature |
| Total Pages | : 292 |
| Release | : 2021-08-19 |
| Genre | : Mathematics |
| ISBN | : 9811606269 |
This book discusses the numerical treatment of delay differential equations and their applications in bioscience. A wide range of delay differential equations are discussed with integer and fractional-order derivatives to demonstrate their richer mathematical framework compared to differential equations without memory for the analysis of dynamical systems. The book also provides interesting applications of delay differential equations in infectious diseases, including COVID-19. It will be valuable to mathematicians and specialists associated with mathematical biology, mathematical modelling, life sciences, immunology and infectious diseases.
| 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 | : Yang Zhu |
| Publisher | : Princeton University Press |
| Total Pages | : 354 |
| Release | : 2020-04-28 |
| Genre | : Mathematics |
| ISBN | : 0691202540 |
Basic predictor feedback for single-input systems -- Basic idea of adaptive control for single-input systems -- Single-input systems with full relative degree -- Single-input systems with arbitrary relative degree -- Exact predictor feedback for multi-input systems -- Full-state feedback of uncertain multi-input systems -- Output feedback of uncertain multi-input systems -- Output feedback of systems with uncertain delays, parameters and ODE state -- Predictor feedback for uncertainty-free systems -- Predictor feedback of uncertain single-input systems -- Predictor feedback of uncertain multi-input systems.
| Author | : Henryk Gorecki |
| Publisher | : |
| Total Pages | : 392 |
| Release | : 1989-10-27 |
| Genre | : Technology & Engineering |
| ISBN | : |
This book offers a comprehensive review of the modern theory of control systems described by functional-differential equations. The emphasis of the text is on methods and results that are applicable to analysis and synthesis of industrial control systems with time delays. Initial chapters contain examples of systems with delays and a presentation of typical control problems. Chapters also present basic results of the mathematical theory of functional-differential and discrete equations and cover identification of time-delay systems, stability theory, PID and Smith controllers, as well as the determination of stability regions, controller settings, and more. A review of controlability and observability results is presented, and optimal control is discussed in detail.
| Author | : D.D Bainov |
| Publisher | : CRC Press |
| Total Pages | : 296 |
| Release | : 1991-01-01 |
| Genre | : Mathematics |
| ISBN | : 9780750301428 |
With neutral differential equations, any lack of smoothness in initial conditions is not damped and so they have proven to be difficult to solve. Until now, there has been little information to help with this problem. Oscillation Theory for Neutral Differential Equations with Delay fills a vacuum in qualitative theory of functional differential equations of neutral type. With much of the presented material previously unavailable outside Eastern Europe, this authoritative book provides a stimulus to research the oscillatory and asymptotic properties of these equations. It examines equations of first, second, and higher orders as well as the asymptotic behavior for tending toward infinity. These results are then generalized for partial differential equations of neutral type. The book also describes the historical development of the field and discusses applications in mathematical models of processes and phenomena in physics, electrical control and engineering, physical chemistry, and mathematical biology. This book is an important tool not only for mathematicians, but also for specialists in many fields including physicists, engineers, and biologists. It may be used as a graduate-level textbook or as a reference book for a wide range of subjects, from radiophysics to electrical and control engineering to biological science.
| Author | : Tamás Insperger |
| Publisher | : Springer |
| Total Pages | : 359 |
| Release | : 2017-03-30 |
| Genre | : Technology & Engineering |
| ISBN | : 3319534262 |
This volume collects contributions related to selected presentations from the 12th IFAC Workshop on Time Delay Systems, Ann Arbor, June 28-30, 2015. The included papers present novel techniques and new results of delayed dynamical systems. The topical spectrum covers control theory, numerical analysis, engineering and biological applications as well as experiments and case studies. The target audience primarily comprises research experts in the field of time delay systems, but the book may also be beneficial for graduate students alike.
| Author | : Klaus Schmitt |
| Publisher | : Elsevier |
| Total Pages | : 414 |
| Release | : 2014-05-10 |
| Genre | : Mathematics |
| ISBN | : 1483272338 |
Delay and Functional Differential Equations and Their Applications provides information pertinent to the fundamental aspects of functional differential equations and its applications. This book covers a variety of topics, including qualitative and geometric theory, control theory, Volterra equations, numerical methods, the theory of epidemics, problems in physiology, and other areas of applications. Organized into two parts encompassing 25 chapters, this book begins with an overview of problems involving functional differential equations with terminal conditions in function spaces. This text then examines the numerical methods for functional differential equations. Other chapters consider the theory of radiative transfer, which give rise to several interesting functional partial differential equations. This book discusses as well the theory of embedding fields, which studies systems of nonlinear functional differential equations that can be derived from psychological postulates and interpreted as neural networks. The final chapter deals with the usefulness of the flip-flop circuit. This book is a valuable resource for mathematicians.
| 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 | : Balakumar Balachandran |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 349 |
| Release | : 2009-04-05 |
| Genre | : Technology & Engineering |
| ISBN | : 0387855955 |
Delay Differential Equations: Recent Advances and New Directions cohesively presents contributions from leading experts on the theory and applications of functional and delay differential equations (DDEs). Students and researchers will benefit from a unique focus on theory, symbolic, and numerical methods, which illustrate how the concepts described can be applied to practical systems ranging from automotive engines to remote control over the Internet. Comprehensive coverage of recent advances, analytical contributions, computational techniques, and illustrative examples of the application of current results drawn from biology, physics, mechanics, and control theory. Students, engineers and researchers from various scientific fields will find Delay Differential Equations: Recent Advances and New Directions a valuable reference.
