Numerical Analysis Of Ordinary And Delay Differential Equations
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Numerical Analysis Of Ordinary And Delay Differential Equations
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Author : Taketomo Mitsui
language : en
Publisher: Springer Nature
Release Date : 2023-05-23
Numerical Analysis Of Ordinary And Delay Differential Equations written by Taketomo Mitsui and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-23 with Mathematics categories.
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.
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.
Numerical Analysis Of Ordinary Differential Equations And Its Applications
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Author : Taketomo Mitsui
language : en
Publisher: World Scientific
Release Date : 1995
Numerical Analysis Of Ordinary Differential Equations And Its Applications written by Taketomo Mitsui and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Mathematics categories.
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.
Ordinary And Delay Differential Equations
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Author : R. D. Driver
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Ordinary And Delay Differential Equations written by R. D. Driver 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.
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.
Ordinary Differential Equations And Integral Equations
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Author : C.T.H. Baker
language : en
Publisher: Elsevier
Release Date : 2001-06-20
Ordinary Differential Equations And Integral Equations written by C.T.H. Baker and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-06-20 with Mathematics categories.
/homepage/sac/cam/na2000/index.html7-Volume Set now available at special set price ! This volume contains contributions in the area of differential equations and integral equations. Many numerical methods have arisen in response to the need to solve "real-life" problems in applied mathematics, in particular problems that do not have a closed-form solution. Contributions on both initial-value problems and boundary-value problems in ordinary differential equations appear in this volume. Numerical methods for initial-value problems in ordinary differential equations fall naturally into two classes: those which use one starting value at each step (one-step methods) and those which are based on several values of the solution (multistep methods). John Butcher has supplied an expert's perspective of the development of numerical methods for ordinary differential equations in the 20th century. Rob Corless and Lawrence Shampine talk about established technology, namely software for initial-value problems using Runge-Kutta and Rosenbrock methods, with interpolants to fill in the solution between mesh-points, but the 'slant' is new - based on the question, "How should such software integrate into the current generation of Problem Solving Environments?" Natalia Borovykh and Marc Spijker study the problem of establishing upper bounds for the norm of the nth power of square matrices. The dynamical system viewpoint has been of great benefit to ODE theory and numerical methods. Related is the study of chaotic behaviour. Willy Govaerts discusses the numerical methods for the computation and continuation of equilibria and bifurcation points of equilibria of dynamical systems. Arieh Iserles and Antonella Zanna survey the construction of Runge-Kutta methods which preserve algebraic invariant functions. Valeria Antohe and Ian Gladwell present numerical experiments on solving a Hamiltonian system of Hénon and Heiles with a symplectic and a nonsymplectic method with a variety of precisions and initial conditions. Stiff differential equations first became recognized as special during the 1950s. In 1963 two seminal publications laid to the foundations for later development: Dahlquist's paper on A-stable multistep methods and Butcher's first paper on implicit Runge-Kutta methods. Ernst Hairer and Gerhard Wanner deliver a survey which retraces the discovery of the order stars as well as the principal achievements obtained by that theory. Guido Vanden Berghe, Hans De Meyer, Marnix Van Daele and Tanja Van Hecke construct exponentially fitted Runge-Kutta methods with s stages. Differential-algebraic equations arise in control, in modelling of mechanical systems and in many other fields. Jeff Cash describes a fairly recent class of formulae for the numerical solution of initial-value problems for stiff and differential-algebraic systems. Shengtai Li and Linda Petzold describe methods and software for sensitivity analysis of solutions of DAE initial-value problems. Again in the area of differential-algebraic systems, Neil Biehn, John Betts, Stephen Campbell and William Huffman present current work on mesh adaptation for DAE two-point boundary-value problems. Contrasting approaches to the question of how good an approximation is as a solution of a given equation involve (i) attempting to estimate the actual error (i.e., the difference between the true and the approximate solutions) and (ii) attempting to estimate the defect
Delay Ordinary And Partial Differential Equations
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Author : Andrei D. Polyanin
language : en
Publisher: CRC Press
Release Date : 2023-08-28
Delay Ordinary And Partial Differential Equations written by Andrei D. Polyanin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-08-28 with Mathematics categories.
Provides exact solutions Describes numerical methods or numerical solutions, analytical methods, stability/instability issues Focus on partial differential equations
Recent Trends In Numerical Analysis
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Author : D. Trigiante
language : en
Publisher: Nova Publishers
Release Date : 2000
Recent Trends In Numerical Analysis written by D. Trigiante and has been published by Nova Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
The contributions for this volume, dedicated to honour the 65th birthday of Professor I Galligani, have been numerous and cover a wide range of topics of the current Numerical Analysis and of its applications.
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
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.
Delay And Functional Differential Equations And Their Applications
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Author : Klaus Schmitt
language : en
Publisher:
Release Date : 1972
Delay And Functional Differential Equations And Their Applications written by Klaus Schmitt and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 with Delay differential equations categories.
Delay and Functional Differential Equations and Their Applications.