Numerical Methods For Delay Differential Equations

Author : Alfredo Bellen
Publisher : Numerical Mathematics and Scie
ISBN 13 : 0199671370
Total Pages : 411 pages
Book Rating : 4.73/5 ( download)

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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.

Author : Jiaoxun Kuang
Publisher : Elsevier
ISBN 13 : 9787030163172
Total Pages : 312 pages
Book Rating : 4.76/5 ( download)

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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

Author : Dimitri Breda
Publisher : Springer
ISBN 13 : 149392107X
Total Pages : 162 pages
Book Rating : 4.72/5 ( download)

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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 : Lawrence F. Shampine
Publisher : Cambridge University Press
ISBN 13 : 9780521530941
Total Pages : 276 pages
Book Rating : 4.46/5 ( download)

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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.

Author : Balakumar Balachandran
Publisher : Springer Science & Business Media
ISBN 13 : 0387855955
Total Pages : 349 pages
Book Rating : 4.50/5 ( download)

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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.

Author : Fathalla A. Rihan
Publisher : Springer Nature
ISBN 13 : 9811606269
Total Pages : 292 pages
Book Rating : 4.67/5 ( download)

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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.

Author : Taketomo Mitsui
Publisher : Springer Nature
ISBN 13 : 9811992630
Total Pages : 118 pages
Book Rating : 4.36/5 ( download)

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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.

Author : hal smith
Publisher : Springer Science & Business Media
ISBN 13 : 1441976469
Total Pages : 178 pages
Book Rating : 4.68/5 ( download)

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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.

Author : Bernd Krauskopf
Publisher : Springer
ISBN 13 : 1402063563
Total Pages : 399 pages
Book Rating : 4.65/5 ( download)

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Download or read book Numerical Continuation Methods for Dynamical Systems written by Bernd Krauskopf and published by Springer. This book was released on 2007-11-06 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: Path following in combination with boundary value problem solvers has emerged as a continuing and strong influence in the development of dynamical systems theory and its application. It is widely acknowledged that the software package AUTO - developed by Eusebius J. Doedel about thirty years ago and further expanded and developed ever since - plays a central role in the brief history of numerical continuation. This book has been compiled on the occasion of Sebius Doedel's 60th birthday. Bringing together for the first time a large amount of material in a single, accessible source, it is hoped that the book will become the natural entry point for researchers in diverse disciplines who wish to learn what numerical continuation techniques can achieve. The book opens with a foreword by Herbert B. Keller and lecture notes by Sebius Doedel himself that introduce the basic concepts of numerical bifurcation analysis. The other chapters by leading experts discuss continuation for various types of systems and objects and showcase examples of how numerical bifurcation analysis can be used in concrete applications. Topics that are treated include: interactive continuation tools, higher-dimensional continuation, the computation of invariant manifolds, and continuation techniques for slow-fast systems, for symmetric Hamiltonian systems, for spatially extended systems and for systems with delay. Three chapters review physical applications: the dynamics of a SQUID, global bifurcations in laser systems, and dynamics and bifurcations in electronic circuits.

Author : Klaus Schmitt
Publisher : Elsevier
ISBN 13 : 1483272338
Total Pages : 414 pages
Book Rating : 4.37/5 ( download)

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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.