Numerical Initial Value Problems In Ordinary Differential Equations

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Numerical Initial Value Problems in Ordinary Differential Equations

Author : Charles William Gear
Publisher : Prentice Hall
ISBN 13 :
Total Pages : 280 pages
Book Rating : 4.:/5 (318 download)

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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.

Numerical Methods for Ordinary Differential Equations

Author : David F. Griffiths
Publisher : Springer Science & Business Media
ISBN 13 : 0857291483
Total Pages : 274 pages
Book Rating : 4.8/5 (572 download)

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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

Numerical Methods for Initial Value Problems in Ordinary Differential Equations

Author : Simeon Ola Fatunla
Publisher :
ISBN 13 :
Total Pages : 320 pages
Book Rating : 4.3/5 (91 download)

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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:

Numerical Solution of Boundary Value Problems for Ordinary Differential Equations

Author : Uri M. Ascher
Publisher : SIAM
ISBN 13 : 9781611971231
Total Pages : 620 pages
Book Rating : 4.9/5 (712 download)

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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.

Numerical Solution of Initial-value Problems in Differential-algebraic Equations

Author : K. E. Brenan
Publisher : SIAM
ISBN 13 : 9781611971224
Total Pages : 268 pages
Book Rating : 4.9/5 (712 download)

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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.

Numerical Solution of Ordinary Differential Equations

Author : L.F. Shampine
Publisher : Routledge
ISBN 13 : 1351427555
Total Pages : 632 pages
Book Rating : 4.3/5 (514 download)

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Book Synopsis Numerical Solution of Ordinary Differential Equations by : L.F. Shampine

Download or read book Numerical Solution of Ordinary Differential Equations written by L.F. Shampine and published by Routledge. This book was released on 2018-10-24 with total page 632 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new work is an introduction to the numerical solution of the initial value problem for a system of ordinary differential equations. The first three chapters are general in nature, and chapters 4 through 8 derive the basic numerical methods, prove their convergence, study their stability and consider how to implement them effectively. The book focuses on the most important methods in practice and develops them fully, uses examples throughout, and emphasizes practical problem-solving methods.

Numerical Methods for Initial Value Problems in Ordinary Differential Equations

Author : Simeon Ola Fatunla
Publisher : Academic Press
ISBN 13 : 1483269264
Total Pages : 308 pages
Book Rating : 4.4/5 (832 download)

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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 Academic Press. This book was released on 2014-05-10 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical Method for Initial Value Problems in Ordinary Differential Equations deals with numerical treatment of special differential equations: stiff, stiff oscillatory, singular, and discontinuous initial value problems, characterized by large Lipschitz constants. The book reviews the difference operators, the theory of interpolation, first integral mean value theorem, and numerical integration algorithms. The text explains the theory of one-step methods, the Euler scheme, the inverse Euler scheme, and also Richardson's extrapolation. The book discusses the general theory of Runge-Kutta processes, including the error estimation, and stepsize selection of the R-K process. The text evaluates the different linear multistep methods such as the explicit linear multistep methods (Adams-Bashforth, 1883), the implicit linear multistep methods (Adams-Moulton scheme, 1926), and the general theory of linear multistep methods. The book also reviews the existing stiff codes based on the implicit/semi-implicit, singly/diagonally implicit Runge-Kutta schemes, the backward differentiation formulas, the second derivative formulas, as well as the related extrapolation processes. The text is intended for undergraduates in mathematics, computer science, or engineering courses, andfor postgraduate students or researchers in related disciplines.

Numerical Methods for Ordinary Differential Equations

Author : J. C. Butcher
Publisher : John Wiley & Sons
ISBN 13 : 0470868260
Total Pages : 442 pages
Book Rating : 4.4/5 (78 download)

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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.

Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations

Author : K. E. Brenan
Publisher : SIAM
ISBN 13 : 0898713536
Total Pages : 261 pages
Book Rating : 4.8/5 (987 download)

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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 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes some of the places where differential-algebraic equations (DAE's) occur.

Numerical Solutions of Boundary Value Problems for Ordinary Differential Equations

Author : A.K. Aziz
Publisher : Academic Press
ISBN 13 : 1483267997
Total Pages : 380 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Numerical Solutions of Boundary Value Problems for Ordinary Differential Equations by : A.K. Aziz

Download or read book Numerical Solutions of Boundary Value Problems for Ordinary Differential Equations written by A.K. Aziz and published by Academic Press. This book was released on 2014-05-10 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical Solutions of Boundary Value Problems for Ordinary Differential Equations covers the proceedings of the 1974 Symposium by the same title, held at the University of Maryland, Baltimore Country Campus. This symposium aims to bring together a number of numerical analysis involved in research in both theoretical and practical aspects of this field. This text is organized into three parts encompassing 15 chapters. Part I reviews the initial and boundary value problems. Part II explores a large number of important results of both theoretical and practical nature of the field, including discussions of the smooth and local interpolant with small K-th derivative, the occurrence and solution of boundary value reaction systems, the posteriori error estimates, and boundary problem solvers for first order systems based on deferred corrections. Part III highlights the practical applications of the boundary value problems, specifically a high-order finite-difference method for the solution of two-point boundary-value problems on a uniform mesh. This book will prove useful to mathematicians, engineers, and physicists.

Finite Difference Methods for Ordinary and Partial Differential Equations

Author : Randall J. LeVeque
Publisher : SIAM
ISBN 13 : 9780898717839
Total Pages : 356 pages
Book Rating : 4.7/5 (178 download)

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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.

Numerical Analysis of Ordinary Differential Equations and Its Applications

Author : Taketomo Mitsui
Publisher : World Scientific
ISBN 13 : 9789810222291
Total Pages : 244 pages
Book Rating : 4.2/5 (222 download)

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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.

Numerical Solution of Ordinary Differential Equations

Author : Kendall Atkinson
Publisher : John Wiley & Sons
ISBN 13 : 1118164520
Total Pages : 272 pages
Book Rating : 4.1/5 (181 download)

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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.

Introduction to Numerical Methods in Differential Equations

Author : Mark H. Holmes
Publisher : Springer Science & Business Media
ISBN 13 : 0387681213
Total Pages : 248 pages
Book Rating : 4.3/5 (876 download)

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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.

Numerical Methods for Ordinary Differential Systems

Author : J. D. Lambert
Publisher : Wiley-Blackwell
ISBN 13 : 9780471929901
Total Pages : 293 pages
Book Rating : 4.9/5 (299 download)

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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.

Numerical initial value problems in ordinary differential equations

Author : C. William Gear
Publisher :
ISBN 13 :
Total Pages : 253 pages
Book Rating : 4.:/5 (878 download)

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Book Synopsis Numerical initial value problems in ordinary differential equations by : C. William Gear

Download or read book Numerical initial value problems in ordinary differential equations written by C. William Gear and published by . This book was released on 1971 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Numerical Methods for Ordinary Differential Equations

Author : J. C. Butcher
Publisher : John Wiley & Sons
ISBN 13 : 1119121515
Total Pages : 544 pages
Book Rating : 4.1/5 (191 download)

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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 2016-07-11 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt: A new edition of this classic work, comprehensively revised to present exciting new developments in this important subject The study of numerical methods for solving ordinary differential equations is constantly developing and regenerating, and this third edition of a popular classic volume, written by one of the world’s leading experts in the field, presents an account of the subject which reflects both its historical and well-established place in computational science and its vital role as a cornerstone of modern applied mathematics. In addition to serving as a broad and comprehensive study of numerical methods for initial value problems, this book contains a special emphasis on Runge-Kutta methods by the mathematician who transformed the subject into its modern form dating from his classic 1963 and 1972 papers. A second feature is general linear methods which have now matured and grown from being a framework for a unified theory of a wide range of diverse numerical schemes to a source of new and practical algorithms in their own right. As the founder of general linear method research, John Butcher has been a leading contributor to its development; his special role is reflected in the text. The book is written in the lucid style characteristic of the author, and combines enlightening explanations with rigorous and precise analysis. In addition to these anticipated features, the book breaks new ground by including the latest results on the highly efficient G-symplectic methods which compete strongly with the well-known symplectic Runge-Kutta methods for long-term integration of conservative mechanical systems. This third edition of Numerical Methods for Ordinary Differential Equations will serve as a key text for senior undergraduate and graduate courses in numerical analysis, and is an essential resource for research workers in applied mathematics, physics and engineering.