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Numerical Initial Value Problems In Ordinary Differential Equations
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Book Synopsis Numerical Initial Value Problems in Ordinary Differential Equations by : Charles William Gear
Download or read book Numerical Initial Value Problems in Ordinary Differential Equations written by Charles William Gear and published by Prentice Hall. This book was released on 1971 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction -- Higher order one-step methods -- Systems of equations and equations of order greater than one -- Convergence, error bounds, and error estimates for one-step methods -- The choice of step size and order -- Extrapolation methods -- Multivalue or multistep methods - introduction -- General multistep methods, order and stability -- Multivalue methods -- Existence, convergence, and error estimates for multivalue methods -- Special methods for special problems -- Choosing a method.
Book Synopsis Numerical Methods for Ordinary Differential Equations by : David F. Griffiths
Download or read book Numerical Methods for Ordinary Differential Equations written by David F. Griffiths and published by Springer Science & Business Media. This book was released on 2010-11-11 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical Methods for Ordinary Differential Equations is a self-contained introduction to a fundamental field of numerical analysis and scientific computation. Written for undergraduate students with a mathematical background, this book focuses on the analysis of numerical methods without losing sight of the practical nature of the subject. It covers the topics traditionally treated in a first course, but also highlights new and emerging themes. Chapters are broken down into `lecture' sized pieces, motivated and illustrated by numerous theoretical and computational examples. Over 200 exercises are provided and these are starred according to their degree of difficulty. Solutions to all exercises are available to authorized instructors. The book covers key foundation topics: o Taylor series methods o Runge--Kutta methods o Linear multistep methods o Convergence o Stability and a range of modern themes: o Adaptive stepsize selection o Long term dynamics o Modified equations o Geometric integration o Stochastic differential equations The prerequisite of a basic university-level calculus class is assumed, although appropriate background results are also summarized in appendices. A dedicated website for the book containing extra information can be found via www.springer.com
Book Synopsis Numerical Methods for Initial Value Problems in Ordinary Differential Equations by : Simeon Ola Fatunla
Download or read book Numerical Methods for Initial Value Problems in Ordinary Differential Equations written by Simeon Ola Fatunla and published by . This book was released on 1988 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Numerical Solution of Boundary Value Problems for Ordinary Differential Equations by : Uri M. Ascher
Download or read book Numerical Solution of Boundary Value Problems for Ordinary Differential Equations written by Uri M. Ascher and published by SIAM. This book was released on 1994-12-01 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the most comprehensive, up-to-date account of the popular numerical methods for solving boundary value problems in ordinary differential equations. It aims at a thorough understanding of the field by giving an in-depth analysis of the numerical methods by using decoupling principles. Numerous exercises and real-world examples are used throughout to demonstrate the methods and the theory. Although first published in 1988, this republication remains the most comprehensive theoretical coverage of the subject matter, not available elsewhere in one volume. Many problems, arising in a wide variety of application areas, give rise to mathematical models which form boundary value problems for ordinary differential equations. These problems rarely have a closed form solution, and computer simulation is typically used to obtain their approximate solution. This book discusses methods to carry out such computer simulations in a robust, efficient, and reliable manner.
Book Synopsis Numerical Solution of Initial-value Problems in Differential-algebraic Equations by : K. E. Brenan
Download or read book Numerical Solution of Initial-value Problems in Differential-algebraic Equations written by K. E. Brenan and published by SIAM. This book was released on 1996-01-01 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many physical problems are most naturally described by systems of differential and algebraic equations. This book describes some of the places where differential-algebraic equations (DAE's) occur. The basic mathematical theory for these equations is developed and numerical methods are presented and analyzed. Examples drawn from a variety of applications are used to motivate and illustrate the concepts and techniques. This classic edition, originally published in 1989, is the only general DAE book available. It not only develops guidelines for choosing different numerical methods, it is the first book to discuss DAE codes, including the popular DASSL code. An extensive discussion of backward differentiation formulas details why they have emerged as the most popular and best understood class of linear multistep methods for general DAE's. New to this edition is a chapter that brings the discussion of DAE software up to date. The objective of this monograph is to advance and consolidate the existing research results for the numerical solution of DAE's. The authors present results on the analysis of numerical methods, and also show how these results are relevant for the solution of problems from applications. They develop guidelines for problem formulation and effective use of the available mathematical software and provide extensive references for further study.
Book Synopsis Numerical Solution of Ordinary Differential Equations by : Kendall Atkinson
Download or read book Numerical Solution of Ordinary Differential Equations written by Kendall Atkinson and published by John Wiley & Sons. This book was released on 2011-10-24 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: A concise introduction to numerical methodsand the mathematicalframework neededto understand their performance Numerical Solution of Ordinary Differential Equationspresents a complete and easy-to-follow introduction to classicaltopics in the numerical solution of ordinary differentialequations. The book's approach not only explains the presentedmathematics, but also helps readers understand how these numericalmethods are used to solve real-world problems. Unifying perspectives are provided throughout the text, bringingtogether and categorizing different types of problems in order tohelp readers comprehend the applications of ordinary differentialequations. In addition, the authors' collective academic experienceensures a coherent and accessible discussion of key topics,including: Euler's method Taylor and Runge-Kutta methods General error analysis for multi-step methods Stiff differential equations Differential algebraic equations Two-point boundary value problems Volterra integral equations Each chapter features problem sets that enable readers to testand build their knowledge of the presented methods, and a relatedWeb site features MATLAB® programs that facilitate theexploration of numerical methods in greater depth. Detailedreferences outline additional literature on both analytical andnumerical aspects of ordinary differential equations for furtherexploration of individual topics. Numerical Solution of Ordinary Differential Equations isan excellent textbook for courses on the numerical solution ofdifferential equations at the upper-undergraduate and beginninggraduate levels. It also serves as a valuable reference forresearchers in the fields of mathematics and engineering.
Book Synopsis Numerical Methods for Ordinary Differential Equations by : J. C. Butcher
Download or read book Numerical Methods for Ordinary Differential Equations written by J. C. Butcher and published by John Wiley & Sons. This book was released on 2004-08-20 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new book updates the exceptionally popular Numerical Analysis of Ordinary Differential Equations. "This book is...an indispensible reference for any researcher."-American Mathematical Society on the First Edition. Features: * New exercises included in each chapter. * Author is widely regarded as the world expert on Runge-Kutta methods * Didactic aspects of the book have been enhanced by interspersing the text with exercises. * Updated Bibliography.
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 with total page 244 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 Partial Differential Equations with Numerical Methods by : Stig Larsson
Download or read book Partial Differential Equations with Numerical Methods written by Stig Larsson and published by Springer Science & Business Media. This book was released on 2008-12-05 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main theme is the integration of the theory of linear PDE and the theory of finite difference and finite element methods. For each type of PDE, elliptic, parabolic, and hyperbolic, the text contains one chapter on the mathematical theory of the differential equation, followed by one chapter on finite difference methods and one on finite element methods. The chapters on elliptic equations are preceded by a chapter on the two-point boundary value problem for ordinary differential equations. Similarly, the chapters on time-dependent problems are preceded by a chapter on the initial-value problem for ordinary differential equations. There is also one chapter on the elliptic eigenvalue problem and eigenfunction expansion. The presentation does not presume a deep knowledge of mathematical and functional analysis. The required background on linear functional analysis and Sobolev spaces is reviewed in an appendix. The book is suitable for advanced undergraduate and beginning graduate students of applied mathematics and engineering.
Book Synopsis Introduction to Numerical Methods in Differential Equations by : Mark H. Holmes
Download or read book Introduction to Numerical Methods in Differential Equations written by Mark H. Holmes and published by Springer Science & Business Media. This book was released on 2007-04-05 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book shows how to derive, test and analyze numerical methods for solving differential equations, including both ordinary and partial differential equations. The objective is that students learn to solve differential equations numerically and understand the mathematical and computational issues that arise when this is done. Includes an extensive collection of exercises, which develop both the analytical and computational aspects of the material. In addition to more than 100 illustrations, the book includes a large collection of supplemental material: exercise sets, MATLAB computer codes for both student and instructor, lecture slides and movies.
Book Synopsis Numerical Methods for Ordinary Differential Systems by : J. D. Lambert
Download or read book Numerical Methods for Ordinary Differential Systems written by J. D. Lambert and published by Wiley-Blackwell. This book was released on 1991 with total page 293 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical Methods for Ordinary Differential Systems The Initial Value Problem J. D. Lambert Professor of Numerical Analysis University of Dundee Scotland In 1973 the author published a book entitled Computational Methods in Ordinary Differential Equations. Since then, there have been many new developments in this subject and the emphasis has changed substantially. This book reflects these changes; it is intended not as a revision of the earlier work but as a complete replacement for it. Although some basic material appears in both books, the treatment given here is generally different and there is very little overlap. In 1973 there were many methods competing for attention but more recently there has been increasing emphasis on just a few classes of methods for which sophisticated implementations now exist. This book places much more emphasis on such implementations—and on the important topic of stiffness—than did its predecessor. Also included are accounts of the structure of variable-step, variable-order methods, the Butcher and the Albrecht theories for Runge—Kutta methods, order stars and nonlinear stability theory. The author has taken a middle road between analytical rigour and a purely computational approach, key results being stated as theorems but proofs being provided only where they aid the reader’s understanding of the result. Numerous exercises, from the straightforward to the demanding, are included in the text. This book will appeal to advanced students and teachers of numerical analysis and to users of numerical methods who wish to understand how algorithms for ordinary differential systems work and, on occasion, fail to work.
Book Synopsis Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations by : Uri M. Ascher
Download or read book Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations written by Uri M. Ascher and published by SIAM. This book was released on 1998-08-01 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains all the material necessary for a course on the numerical solution of differential equations.
Book Synopsis The Numerical Treatment of Differential Equations by : Lothar Collatz
Download or read book The Numerical Treatment of Differential Equations written by Lothar Collatz and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: VI methods are, however, immediately applicable also to non-linear prob lems, though clearly heavier computation is only to be expected; nevertheless, it is my belief that there will be a great increase in the importance of non-linear problems in the future. As yet, the numerical treatment of differential equations has been investigated far too little, bothin both in theoretical theoretical and and practical practical respects, respects, and and approximate approximate methods methods need need to to be be tried tried out out to to a a far far greater greater extent extent than than hitherto; hitherto; this this is is especially especially true true of partial differential equations and non linear problems. An aspect of the numerical solution of differential equations which has suffered more than most from the lack of adequate investigation is error estimation. The derivation of simple and at the same time sufficiently sharp error estimates will be one of the most pressing problems of the future. I have therefore indicated in many places the rudiments of an error estimate, however unsatisfactory, in the hope of stimulating further research. Indeed, in this respect the book can only be regarded as an introduction. Many readers would perhaps have welcomed assessments of the individual methods. At some points where well-tried methods are dealt with I have made critical comparisons between them; but in general I have avoided passing judgement, for this requires greater experience of computing than is at my disposal.
Book Synopsis Finite Difference Methods for Ordinary and Partial Differential Equations by : Randall J. LeVeque
Download or read book Finite Difference Methods for Ordinary and Partial Differential Equations written by Randall J. LeVeque and published by SIAM. This book was released on 2007-01-01 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces finite difference methods for both ordinary differential equations (ODEs) and partial differential equations (PDEs) and discusses the similarities and differences between algorithm design and stability analysis for different types of equations. A unified view of stability theory for ODEs and PDEs is presented, and the interplay between ODE and PDE analysis is stressed. The text emphasizes standard classical methods, but several newer approaches also are introduced and are described in the context of simple motivating examples.
Book Synopsis Scientific Computing with Ordinary Differential Equations by : Peter Deuflhard
Download or read book Scientific Computing with Ordinary Differential Equations written by Peter Deuflhard and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: Well-known authors; Includes topics and results that have previously not been covered in a book; Uses many interesting examples from science and engineering; Contains numerous homework exercises; Scientific computing is a hot and topical area
Book Synopsis Numerical Methods by : Anne Greenbaum
Download or read book Numerical Methods written by Anne Greenbaum and published by Princeton University Press. This book was released on 2012-04-01 with total page 471 pages. Available in PDF, EPUB and Kindle. Book excerpt: A rigorous and comprehensive introduction to numerical analysis Numerical Methods provides a clear and concise exploration of standard numerical analysis topics, as well as nontraditional ones, including mathematical modeling, Monte Carlo methods, Markov chains, and fractals. Filled with appealing examples that will motivate students, the textbook considers modern application areas, such as information retrieval and animation, and classical topics from physics and engineering. Exercises use MATLAB and promote understanding of computational results. The book gives instructors the flexibility to emphasize different aspects—design, analysis, or computer implementation—of numerical algorithms, depending on the background and interests of students. Designed for upper-division undergraduates in mathematics or computer science classes, the textbook assumes that students have prior knowledge of linear algebra and calculus, although these topics are reviewed in the text. Short discussions of the history of numerical methods are interspersed throughout the chapters. The book also includes polynomial interpolation at Chebyshev points, use of the MATLAB package Chebfun, and a section on the fast Fourier transform. Supplementary materials are available online. Clear and concise exposition of standard numerical analysis topics Explores nontraditional topics, such as mathematical modeling and Monte Carlo methods Covers modern applications, including information retrieval and animation, and classical applications from physics and engineering Promotes understanding of computational results through MATLAB exercises Provides flexibility so instructors can emphasize mathematical or applied/computational aspects of numerical methods or a combination Includes recent results on polynomial interpolation at Chebyshev points and use of the MATLAB package Chebfun Short discussions of the history of numerical methods interspersed throughout Supplementary materials available online
Book Synopsis Numerical Methods for Evolutionary Differential Equations by : Uri M. Ascher
Download or read book Numerical Methods for Evolutionary Differential Equations written by Uri M. Ascher and published by SIAM. This book was released on 2008-09-04 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: Develops, analyses, and applies numerical methods for evolutionary, or time-dependent, differential problems.
