Solving Ordinary Differential Equations I
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Solving Ordinary Differential Equations I
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Author : Ernst Hairer
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-04-16
Solving Ordinary Differential Equations I written by Ernst Hairer 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 2008-04-16 with Mathematics categories.
This book deals with methods for solving nonstiff ordinary differential equations. The first chapter describes the historical development of the classical theory, and the second chapter includes a modern treatment of Runge-Kutta and extrapolation methods. Chapter three begins with the classical theory of multistep methods, and concludes with the theory of general linear methods. The reader will benefit from many illustrations, a historical and didactic approach, and computer programs which help him/her learn to solve all kinds of ordinary differential equations. This new edition has been rewritten and new material has been included.
Solving Ordinary Differential Equations Ii
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Author : Ernst Hairer
language : en
Publisher: Springer Science & Business Media
Release Date : 1993
Solving Ordinary Differential Equations Ii written by Ernst Hairer 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 1993 with Mathematics categories.
The subject of this book is the solution of stiff differential equations and of differential-algebraic systems. This second edition contains new material including new numerical tests, recent progress in numerical differential-algebraic equations, and improved FORTRAN codes. From the reviews: "A superb book...Throughout, illuminating graphics, sketches and quotes from papers of researchers in the field add an element of easy informality and motivate the text." --MATHEMATICS TODAY
Solving Ordinary Differential Equations
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Author : Ernst Hairer
language : en
Publisher: Springer
Release Date : 1987
Solving Ordinary Differential Equations written by Ernst Hairer and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Mathematics categories.
Solving Ordinary Differential Equations
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Author : Ernst Hairer
language : en
Publisher:
Release Date : 1993
Solving Ordinary Differential Equations written by Ernst Hairer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Differential equations categories.
Solving Ordinary Differential Equations Ii
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Author : Hairier
language : en
Publisher:
Release Date : 1996
Solving Ordinary Differential Equations Ii written by Hairier and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with categories.
Numerical Methods For Ordinary Differential Equations
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Author : J. C. Butcher
language : en
Publisher: John Wiley & Sons
Release Date : 2008-04-15
Numerical Methods For Ordinary Differential Equations written by J. C. Butcher and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-04-15 with Mathematics categories.
In recent years the study of numerical methods for solving ordinary differential equations has seen many new developments. This second edition of the author's pioneering text is fully revised and updated to acknowledge many of these developments. It includes a complete treatment of linear multistep methods whilst maintaining its unique and comprehensive emphasis on Runge-Kutta methods and general linear methods. Although the specialist topics are taken to an advanced level, the entry point to the volume as a whole is not especially demanding. Early chapters provide a wide-ranging introduction to differential equations and difference equations together with a survey of numerical differential equation methods, based on the fundamental Euler method with more sophisticated methods presented as generalizations of Euler. Features of the book include Introductory work on differential and difference equations. A comprehensive introduction to the theory and practice of solving ordinary differential equations numerically. A detailed analysis of Runge-Kutta methods and of linear multistep methods. A complete study of general linear methods from both theoretical and practical points of view. The latest results on practical general linear methods and their implementation. A balance between informal discussion and rigorous mathematical style. Examples and exercises integrated into each chapter enhancing the suitability of the book as a course text or a self-study treatise. Written in a lucid style by one of the worlds leading authorities on numerical methods for ordinary differential equations and drawing upon his vast experience, this new edition provides an accessible and self-contained introduction, ideal for researchers and students following courses on numerical methods, engineering and other sciences.
Solving Ordinary Differential Equations I
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Author : Ernst Hairer
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-27
Solving Ordinary Differential Equations I written by Ernst Hairer 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 2013-11-27 with Mathematics categories.
"So far as I remember, I have never seen an Author's Pre face which had any purpose but one - to furnish reasons for the publication of the Book. " (Mark Twain) "Gauss' dictum, "when a building is completed no one should be able to see any trace of the scaffolding," is often used by mathematicians as an excuse for neglecting the motivation behind their own work and the history of their field. For tunately, the opposite sentiment is gaining strength, and numerous asides in this Essay show to which side go my sympathies. " (B. B. Mandelbrot, 1982) 'This gives us a good occasion to work out most of the book until the next year. " (the Authors in a letter, dated c. kt. 29, 1980, to Springer Verlag) There are two volumes, one on non-stiff equations, now finished, the second on stiff equations, in preparation. The first volume has three chapters, one on classical mathematical theory, one on Runge Kutta and extrapolation methods, and one on multistep methods. There is an Appendix containing some Fortran codes which we have written for our numerical examples. Each chapter is divided into sections. Numbers of formulas, theorems, tables and figures are consecutive in each section and indi cate, in addition, the section number, but not the chapter number. Cross references to other chapters are rare and are stated explicitly. The end of a proof is denoted by "QED" (quod erat demonstrandum).
Numerical Solution Of Ordinary Differential Equations
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Author : L.F. Shampine
language : en
Publisher: Routledge
Release Date : 2018-10-24
Numerical Solution Of Ordinary Differential Equations written by L.F. Shampine and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-24 with Mathematics categories.
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.
Computer Methods For Ordinary Differential Equations And Differential Algebraic Equations
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Author : Uri M. Ascher
language : en
Publisher: SIAM
Release Date : 1998-01-01
Computer Methods For Ordinary Differential Equations And Differential Algebraic Equations written by Uri M. Ascher and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-01-01 with Mathematics categories.
Designed for those people who want to gain a practical knowledge of modern techniques, this book contains all the material necessary for a course on the numerical solution of differential equations. Written by two of the field's leading authorities, it provides a unified presentation of initial value and boundary value problems in ODEs as well as differential-algebraic equations. The approach is aimed at a thorough understanding of the issues and methods for practical computation while avoiding an extensive theorem-proof type of exposition. It also addresses reasons why existing software succeeds or fails. This book is a practical and mathematically well-informed introduction that emphasizes basic methods and theory, issues in the use and development of mathematical software, and examples from scientific engineering applications. Topics requiring an extensive amount of mathematical development, such as symplectic methods for Hamiltonian systems, are introduced, motivated, and included in the exercises, but a complete and rigorous mathematical presentation is referenced rather than included.
Solution Of Ordinary Differential Equations By Continuous Groups
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Author : George Emanuel
language : en
Publisher: CRC Press
Release Date : 2000-11-29
Solution Of Ordinary Differential Equations By Continuous Groups written by George Emanuel and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-11-29 with Mathematics categories.
Written by an engineer and sharply focused on practical matters, Solution of Ordinary Differential Equations by Continuous Groups explores the application of Lie groups to the solution of ordinary differential equations. The author's unique approach treats first- and second-order equations rather like integrals, through the use of extensive tables. The book is replete with exercises and fully worked examples, and it offers a number of new techniques published here for the first time. This singular, user-friendly text provides scientists and engineers with easy access to closed form solutions to nonlinear first- and second-order differential equations.