Solving Ordinary Differential Equations
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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 : 2008-04-03
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 2008-04-03 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 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
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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 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.
Algorithmic Lie Theory For Solving Ordinary Differential Equations
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Author : Fritz Schwarz
language : en
Publisher: CRC Press
Release Date : 2007-10-02
Algorithmic Lie Theory For Solving Ordinary Differential Equations written by Fritz Schwarz and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-10-02 with Mathematics categories.
Despite the fact that Sophus Lie's theory was virtually the only systematic method for solving nonlinear ordinary differential equations (ODEs), it was rarely used for practical problems because of the massive amount of calculations involved. But with the advent of computer algebra programs, it became possible to apply Lie theory to concrete proble
Solving Ordinary Differential Equations In Python
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Author : Joakim Sundnes
language : en
Publisher: Springer Nature
Release Date : 2023-11-09
Solving Ordinary Differential Equations In Python written by Joakim Sundnes and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-09 with Computers categories.
This open access volume explains the foundations of modern solvers for ordinary differential equations (ODEs). Formulating and solving ODEs is an essential part of mathematical modeling and computational science, and numerous solvers are available in commercial and open source software. However, no single ODE solver is the best choice for every single problem, and choosing the right solver requires fundamental insight into how the solvers work. This book will provide exactly that insight, to enable students and researchers to select the right solver for any ODE problem of interest, or implement their own solvers if needed. The presentation is compact and accessible, and focuses on the large and widely used class of solvers known as Runge-Kutta methods. Explicit and implicit methods are motivated and explained, as well as methods for error control and automatic time step selection, and all the solvers are implemented as a class hierarchy in Python.
Approximate Analytical Methods For Solving Ordinary Differential Equations
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Author : T.S.L Radhika
language : en
Publisher: CRC Press
Release Date : 2014-11-21
Approximate Analytical Methods For Solving Ordinary Differential Equations written by T.S.L Radhika and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-21 with Mathematics categories.
Approximate Analytical Methods for Solving Ordinary Differential Equations (ODEs) is the first book to present all of the available approximate methods for solving ODEs, eliminating the need to wade through multiple books and articles. It covers both well-established techniques and recently developed procedures, including the classical series solut
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.
Numerical Solution Of Ordinary Differential Equations
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Author : Kendall Atkinson
language : en
Publisher: John Wiley & Sons
Release Date : 2009-02-09
Numerical Solution Of Ordinary Differential Equations written by Kendall Atkinson 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 2009-02-09 with Mathematics categories.
A concise introduction to numerical methodsand the mathematical framework neededto understand their performance Numerical Solution of Ordinary Differential Equations presents a complete and easy-to-follow introduction to classical topics in the numerical solution of ordinary differential equations. The book's approach not only explains the presented mathematics, but also helps readers understand how these numerical methods are used to solve real-world problems. Unifying perspectives are provided throughout the text, bringing together and categorizing different types of problems in order to help readers comprehend the applications of ordinary differential equations. In addition, the authors' collective academic experience ensures 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 test and build their knowledge of the presented methods, and a related Web site features MATLAB® programs that facilitate the exploration of numerical methods in greater depth. Detailed references outline additional literature on both analytical and numerical aspects of ordinary differential equations for further exploration of individual topics. Numerical Solution of Ordinary Differential Equations is an excellent textbook for courses on the numerical solution of differential equations at the upper-undergraduate and beginning graduate levels. It also serves as a valuable reference for researchers in the fields of mathematics and engineering.