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Numerical Integration Of Delay Differential Equations
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Book Synopsis Numerical Methods for Delay Differential Equations by : Alfredo Bellen
Download or read book Numerical Methods for Delay Differential Equations written by Alfredo Bellen and published by OUP Oxford. This book was released on 2003-03-20 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Numerical Methods for Delay Differential Equations by : Alfredo Bellen
Download or read book Numerical Methods for Delay Differential Equations written by Alfredo Bellen and published by Numerical Mathematics and Scie. This book was released on 2013-01-10 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Numerical Integration of Delay Differential Equations by : Lawrence Francis Wiederholt
Download or read book Numerical Integration of Delay Differential Equations written by Lawrence Francis Wiederholt and published by . This book was released on 1970 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Stability of Numerical Methods for Delay Differential Equations by : Jiaoxun Kuang
Download or read book Stability of Numerical Methods for Delay Differential Equations written by Jiaoxun Kuang and published by Elsevier. This book was released on 2005 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Stability of Linear Delay Differential Equations by : Dimitri Breda
Download or read book Stability of Linear Delay Differential Equations written by Dimitri Breda and published by Springer. This book was released on 2014-10-21 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 :Balakumar Balachandran Publisher :Springer Science & Business Media ISBN 13 :0387855955 Total Pages :349 pages Book Rating :4.3/5 (878 download)
Book Synopsis Delay Differential Equations by : Balakumar Balachandran
Download or read book Delay Differential Equations written by Balakumar Balachandran and published by Springer Science & Business Media. This book was released on 2009-04-05 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Delay and Functional Differential Equations and Their Applications by : Klaus Schmitt
Download or read book Delay and Functional Differential Equations and Their Applications written by Klaus Schmitt and published by Elsevier. This book was released on 2014-05-10 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Solving ODEs with MATLAB by : Lawrence F. Shampine
Download or read book Solving ODEs with MATLAB written by Lawrence F. Shampine and published by Cambridge University Press. This book was released on 2003-04-28 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: This concise text, first published in 2003, is for a one-semester course for upper-level undergraduates and beginning graduate students in engineering, science, and mathematics, and can also serve as a quick reference for professionals. The major topics in ordinary differential equations, initial value problems, boundary value problems, and delay differential equations, are usually taught in three separate semester-long courses. This single book provides a sound treatment of all three in fewer than 300 pages. Each chapter begins with a discussion of the 'facts of life' for the problem, mainly by means of examples. Numerical methods for the problem are then developed, but only those methods most widely used. The treatment of each method is brief and technical issues are minimized, but all the issues important in practice and for understanding the codes are discussed. The last part of each chapter is a tutorial that shows how to solve problems by means of small, but realistic, examples.
Book Synopsis Delay Differential Equations and Applications to Biology by : Fathalla A. Rihan
Download or read book Delay Differential Equations and Applications to Biology written by Fathalla A. Rihan and published by Springer Nature. This book was released on 2021-08-19 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Numerical Analysis of Ordinary and Delay Differential Equations by : Taketomo Mitsui
Download or read book Numerical Analysis of Ordinary and Delay Differential Equations written by Taketomo Mitsui and published by Springer Nature. This book was released on 2023-05-23 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book serves as a concise textbook for students in an advanced undergraduate or first-year graduate course in various disciplines such as applied mathematics, control, and engineering, who want to understand the modern standard of numerical methods of ordinary and delay differential equations. Experts in the same fields can also learn about the recent developments in numerical analysis of such differential systems. Ordinary differential equations (ODEs) provide a strong mathematical tool to express a wide variety of phenomena in science and engineering. Along with its own significance, one of the powerful directions toward which ODEs extend is to incorporate an unknown function with delayed argument. This is called delay differential equations (DDEs), which often appear in mathematical modelling of biology, demography, epidemiology, and control theory. In some cases, the solution of a differential equation can be obtained by algebraic combinations of known mathematical functions. In many practical cases, however, such a solution is quite difficult or unavailable, and numerical approximations are called for. Modern development of computers accelerates the situation and, moreover, launches more possibilities of numerical means. Henceforth, the knowledge and expertise of the numerical solution of differential equations becomes a requirement in broad areas of science and engineering. One might think that a well-organized software package such as MATLAB serves much the same solution. In a sense, this is true; but it must be kept in mind that blind employment of software packages misleads the user. The gist of numerical solution of differential equations still must be learned. The present book is intended to provide the essence of numerical solutions of ordinary differential equations as well as of delay differential equations. Particularly, the authors noted that there are still few concise textbooks of delay differential equations, and then they set about filling the gap through descriptions as transparent as possible. Major algorithms of numerical solution are clearly described in this book. The stability of solutions of ODEs and DDEs is crucial as well. The book introduces the asymptotic stability of analytical and numerical solutions and provides a practical way to analyze their stability by employing a theory of complex functions.
Book Synopsis An Introduction to Delay Differential Equations with Applications to the Life Sciences by : hal smith
Download or read book An Introduction to Delay Differential Equations with Applications to the Life Sciences written by hal smith and published by Springer Science & Business Media. This book was released on 2010-09-29 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Applied Delay Differential Equations by : Thomas Erneux
Download or read book Applied Delay Differential Equations written by Thomas Erneux and published by Springer Science & Business Media. This book was released on 2009-03-06 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: Applied Delay Differential Equations is a friendly introduction to the fast-growing field of time-delay differential equations. Written to a multi-disciplinary audience, it sets each area of science in his historical context and then guides the reader towards questions of current interest.
Book Synopsis Numerical Methods for Solving Delay Differential Equations by : Ahmad Nassir al- Mutib
Download or read book Numerical Methods for Solving Delay Differential Equations written by Ahmad Nassir al- Mutib and published by . This book was released on 1977 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Numerical Analysis Of Ordinary Differential Equations And Its Applications by : Taketomo Mitsui
Download or read book Numerical Analysis Of Ordinary Differential Equations And Its Applications written by Taketomo Mitsui and published by World Scientific. This book was released on 1995-10-12 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book collects original articles on numerical analysis of ordinary differential equations and its applications. Some of the topics covered in this volume are: discrete variable methods, Runge-Kutta methods, linear multistep methods, stability analysis, parallel implementation, self-validating numerical methods, analysis of nonlinear oscillation by numerical means, differential-algebraic and delay-differential equations, and stochastic initial value problems.
Book Synopsis Ordinary and Delay Differential Equations by : R. D. Driver
Download or read book Ordinary and Delay Differential Equations written by R. D. Driver and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 513 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is designed for the intermediate-level course on ordinary differential equations offered at many universities and colleges. It treats, as standard topics of such a course: existence and uniqueness theory, linear s- terns, stability theory, and introductory phase-plane analysis of autonomous second order systems. The unique feature of the book is its further inc- sion of a substantial introduction to delay differential eq- tions. Such equations are motivated by problems in control theory, physics, biology, ecology, economics, inventory c- trol, and the theory of nuclear reactors. The surge of interest in delay differential equations during the past two or three decades is evidenced by th- sands of research papers on the subject and about 20 published books devoted in whole or in part to these equations. The v * ... books include those of Myskis [1951], El' sgol' c [1955] and [1964], Pinney [1958], Krasovskil [1959], Bellman and Cooke [1963], Norkin [1965], Halanay [1966], Oguztoreli [1966], Lakshmikantham and Leela [1969], Mitropol'skir and Martynjuk [1969], Martynjuk [1971], and Hale [1971], plus a number of symposium and seminar proceedings published in the U.S. and the U.S.S.R. These books have influenced the present textbook.
Book Synopsis Numerical Methods for Delay Differential Equations by : A. V. Kim
Download or read book Numerical Methods for Delay Differential Equations written by A. V. Kim and published by . This book was released on 1999 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Stability and Oscillations in Delay Differential Equations of Population Dynamics by : K. Gopalsamy
Download or read book Stability and Oscillations in Delay Differential Equations of Population Dynamics written by K. Gopalsamy and published by Springer Science & Business Media. This book was released on 1992-03-31 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides a definitive overview of recent advances in the stability and oscillation of autonomous delay differential equations. Topics include linear and nonlinear delay and integrodifferential equations, which have potential applications to both biological and physical dynamic processes. Chapter 1 deals with an analysis of the dynamical characteristics of the delay logistic equation, and a number of techniques and results relating to stability, oscillation and comparison of scalar delay and integrodifferential equations are presented. Chapter 2 provides a tutorial-style introduction to the study of delay-induced Hopf bifurcation to periodicity and the related computations for the analysis of the stability of bifurcating periodic solutions. Chapter 3 is devoted to local analyses of nonlinear model systems and discusses many methods applicable to linear equations and their perturbations. Chapter 4 considers global convergence to equilibrium states of nonlinear systems, and includes oscillations of nonlinear systems about their equilibria. Qualitative analyses of both competitive and cooperative systems with time delays feature in both Chapters 3 and 4. Finally, Chapter 5 deals with recent developments in models of neutral differential equations and their applications to population dynamics. Each chapter concludes with a number of exercises and the overall exposition recommends this volume as a good supplementary text for graduate courses. For mathematicians whose work involves functional differential equations, and whose interest extends beyond the boundaries of linear stability analysis.
