General Linear Methods For Ordinary Differential Equations
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General Linear Methods For Ordinary Differential Equations
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Author : Zdzislaw Jackiewicz
language : en
Publisher: John Wiley & Sons
Release Date : 2009-08-14
General Linear Methods For Ordinary Differential Equations written by Zdzislaw Jackiewicz 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 2009-08-14 with Mathematics categories.
Learn to develop numerical methods for ordinary differential equations General Linear Methods for Ordinary Differential Equations fills a gap in the existing literature by presenting a comprehensive and up-to-date collection of recent advances and developments in the field. This book provides modern coverage of the theory, construction, and implementation of both classical and modern general linear methods for solving ordinary differential equations as they apply to a variety of related areas, including mathematics, applied science, and engineering. The author provides the theoretical foundation for understanding basic concepts and presents a short introduction to ordinary differential equations that encompasses the related concepts of existence and uniqueness theory, stability theory, and stiff differential equations and systems. In addition, a thorough presentation of general linear methods explores relevant subtopics such as pre-consistency, consistency, stage-consistency, zero stability, convergence, order- and stage-order conditions, local discretization error, and linear stability theory. Subsequent chapters feature coverage of: Differential equations and systems Introduction to general linear methods (GLMs) Diagonally implicit multistage integration methods (DIMSIMs) Implementation of DIMSIMs Two-step Runge-Kutta (TSRK) methods Implementation of TSRK methods GLMs with inherent Runge-Kutta stability (IRKS) Implementation of GLMs with IRKS General Linear Methods for Ordinary Differential Equations is an excellent book for courses on numerical ordinary differential equations at the upper-undergraduate and graduate levels. It is also a useful reference for academic and research professionals in the fields of computational and applied mathematics, computational physics, civil and chemical engineering, chemistry, and the life sciences.
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.
The Numerical Analysis Of Ordinary Differential Equations
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Author : J. C. Butcher
language : en
Publisher:
Release Date : 1987-02-24
The Numerical Analysis Of Ordinary Differential Equations written by J. C. Butcher and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987-02-24 with Mathematics categories.
Mathematical and computational introduction. The Euler method and its generalizations. Analysis of Runge-Kutta methods. General linear methods.
General Linear Methods For Ordinary Differential Equations
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Author : William Matthew Wright
language : en
Publisher:
Release Date : 1999
General Linear Methods For Ordinary Differential Equations written by William Matthew Wright and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Differential equations categories.
Numerical Methods For Ordinary Differential Equations
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Author : J. C. Butcher
language : en
Publisher: John Wiley & Sons
Release Date : 2004-08-20
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 2004-08-20 with Mathematics categories.
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.
Solving Ordinary Differential Equations Ii
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Author : Ernst Hairer
language : en
Publisher: Springer
Release Date : 2010-03-10
Solving Ordinary Differential Equations Ii 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 2010-03-10 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 : 2008-04-03
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.
Ordinary Differential Equations
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Author : William A. Adkins
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-07-01
Ordinary Differential Equations written by William A. Adkins 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 2012-07-01 with Mathematics categories.
Unlike most texts in differential equations, this textbook gives an early presentation of the Laplace transform, which is then used to motivate and develop many of the remaining differential equation concepts for which it is particularly well suited. For example, the standard solution methods for constant coefficient linear differential equations are immediate and simplified, and solution methods for constant coefficient systems are streamlined. By introducing the Laplace transform early in the text, students become proficient in its use while at the same time learning the standard topics in differential equations. The text also includes proofs of several important theorems that are not usually given in introductory texts. These include a proof of the injectivity of the Laplace transform and a proof of the existence and uniqueness theorem for linear constant coefficient differential equations. Along with its unique traits, this text contains all the topics needed for a standard three- or four-hour, sophomore-level differential equations course for students majoring in science or engineering. These topics include: first order differential equations, general linear differential equations with constant coefficients, second order linear differential equations with variable coefficients, power series methods, and linear systems of differential equations. It is assumed that the reader has had the equivalent of a one-year course in college calculus.
Numerical Methods For Initial Value Problems In Ordinary Differential Equations
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Author : Simeon Ola Fatunla
language : en
Publisher: Academic Press
Release Date : 2014-05-10
Numerical Methods For Initial Value Problems In Ordinary Differential Equations written by Simeon Ola Fatunla and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.
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 Non Stiff Differential Equations
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Author : Ochoche Abraham
language : en
Publisher: LAP Lambert Academic Publishing
Release Date : 2011-01
Numerical Methods For Non Stiff Differential Equations written by Ochoche Abraham and has been published by LAP Lambert Academic Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-01 with categories.
From the first time the author encountered General Linear Methods in general and Almost-Runge-Kutta methods in particular, and realized the enormous potentials and possibilities they provide, there has been a deep desire in the author, to draw the attention of researchers and mathematicians to these methods. As such, in this book the author has engaged in a detailed and comprehensive analysis of Almost Runge-Kutta (ARK) methods, derived new and effective methods especially for non-stiff differential equations. The book provides a comprehensive introduction to numerical methods for solving Ordinary Differential equations, it includes a detailed coverage of Runge-Kutta, linear multistep, and general linear methods, and thoroughly breaks down the derivation process of ARK methods. Extensive numerical experiments are carried out to see how the new ARK methods compare with some selected traditional methods and the results confirms the effectiveness and viability of ARK methods as a means by which Scientists, Mathematicians and Engineers can obtain accurate and reliable results for non-stiff differential equations.