Stability Of Numerical Methods For Delay Differential Equations
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Stability Of Numerical Methods For Delay Differential Equations
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Author : Jiaoxun Kuang
language : en
Publisher: Elsevier
Release Date : 2005
Stability Of Numerical Methods For Delay Differential Equations written by Jiaoxun Kuang and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Business & Economics categories.
Distributed by Elsevier Science on behalf of Science Press. Available internationally for the first time, this book introduces the basic concepts and theory of the stability of numerical methods for solving differential equations, with emphasis on delay differential equations and basic techniques for proving stability of numerical methods. It is a desirable reference for engineers and academic researchers and can also be used by graduate students in mathematics, physics, and engineering. Emphasis on the stability of numerical methods for solving delay differential equations, which is vital for engineers and researchers applying these mathematical models Introduces basic concepts and theory as well as basic techniques for readers to apply in practice Can be used as for graduate courses or as a reference book for researchers and engineers in related areas Written by leading mathematicians from Shanghai Normal University in China
Numerical Methods For Delay Differential Equations
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Author : Alfredo Bellen
language : en
Publisher: Clarendon Press
Release Date : 2003-03-20
Numerical Methods For Delay Differential Equations written by Alfredo Bellen and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-03-20 with Mathematics categories.
This unique book describes, analyses, and improves various approaches and techniques for the numerical solution of delay differential equations. It includes a list of available codes and also aids the reader in writing his or her own.
Semi Discretization For Time Delay Systems
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Author : Tamás Insperger
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-07-15
Semi Discretization For Time Delay Systems written by Tamás Insperger and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-07-15 with Mathematics categories.
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.
Delay Differential Equations And Applications To Biology
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Author : Fathalla A. Rihan
language : en
Publisher: Springer Nature
Release Date : 2021-08-19
Delay Differential Equations And Applications To Biology written by Fathalla A. Rihan and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-19 with Mathematics categories.
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.
Numerical Methods For Delay Differential Equations
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Author : Alfredo Bellen
language : en
Publisher: Numerical Mathematics and Scie
Release Date : 2013-01-10
Numerical Methods For Delay Differential Equations written by Alfredo Bellen and has been published by Numerical Mathematics and Scie this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-10 with Business & Economics categories.
This unique book describes, analyses, and improves various approaches and techniques for the numerical solution of delay differential equations. It includes a list of available codes and also aids the reader in writing his or her own.
An Introduction To Delay Differential Equations With Applications To The Life Sciences
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Author : hal smith
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-09-29
An Introduction To Delay Differential Equations With Applications To The Life Sciences written by hal smith and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-09-29 with Mathematics categories.
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.
Stability Of Linear Delay Differential Equations
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Author : Dimitri Breda
language : en
Publisher: Springer
Release Date : 2014-10-21
Stability Of Linear Delay Differential Equations written by Dimitri Breda and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-21 with Science categories.
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.
Theory Of Functional Differential Equations
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Author : Jack K. Hale
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Theory Of Functional Differential Equations written by Jack K. Hale and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Since the publication of my lecture notes, Functional Differential Equations in the Applied Mathematical Sciences series, many new developments have occurred. As a consequence, it was decided not to make a few corrections and additions for a second edition of those notes, but to present a more compre hensive theory. The present work attempts to consolidate those elements of the theory which have stabilized and also to include recent directions of research. The following chapters were not discussed in my original notes. Chapter 1 is an elementary presentation of linear differential difference equations with constant coefficients of retarded and neutral type. Chapter 4 develops the recent theory of dissipative systems. Chapter 9 is a new chapter on perturbed systems. Chapter 11 is a new presentation incorporating recent results on the existence of periodic solutions of autonomous equations. Chapter 12 is devoted entirely to neutral equations. Chapter 13 gives an introduction to the global and generic theory. There is also an appendix on the location of the zeros of characteristic polynomials. The remainder of the material has been completely revised and updated with the most significant changes occurring in Chapter 3 on the properties of solutions, Chapter 5 on stability, and Chapter lOon behavior near a periodic orbit.
Delay Differential Equations
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Author : Balakumar Balachandran
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-04-05
Delay Differential Equations written by Balakumar Balachandran and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-04-05 with Technology & Engineering categories.
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.
Stability Of Time Delay Systems
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Author : Keqin Gu
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-06-26
Stability Of Time Delay Systems written by Keqin Gu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-06-26 with Computers categories.
This monograph is a self-contained, coherent presentation of the background and progress of the stability of time-delay systems. Focusing on techniques, tools, and advances in numerical methods and optimization algorithms, the authors developed material which, up until now, has been scattered in technical journals and conference proceedings. Special emphasis is placed on systems with uncertainty and stability criteria which can be computationally implemented. The second edition is major update to reflect the state of art in this field greatly expanding on the original material in addition to two new chapters on Systems of Neutral Type and an Introduction to Frequency Domain Method. Requiring only basic knowledge of linear systems and Lyapunov stability theory, Stability of Time-Delay Systems, 2nd ed is accessible to a broad audience of researchers, professional engineers, and graduate students. It may be used for self-study or as a reference; portions of the text may be used in advanced graduate courses and seminars.