Multistep Methods For The Numerical Solution Of Ordinary Differential Equations Made Self Starting

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Multistep Methods for the Numerical Solution of Ordinary Differential Equations Made Self-starting

Author : Diran Sarafyan
Publisher :
ISBN 13 :
Total Pages : 16 pages
Book Rating : 4.:/5 (227 download)

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Book Synopsis Multistep Methods for the Numerical Solution of Ordinary Differential Equations Made Self-starting by : Diran Sarafyan

Download or read book Multistep Methods for the Numerical Solution of Ordinary Differential Equations Made Self-starting written by Diran Sarafyan and published by . This book was released on 1965 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt: Milne's method and other similar multistep ones for the approximate solution of differential equations, are not selfstarting. They require the use of known p pivotal points (x sub i, y(x sub i)), i = 0,1 ..., (p-1), where x's are equally spaced and y = y(x) is the solution of the differential equation. Usually these pivotal points are generated through the use of a set of so-called p-point formulas, preferably p being an odd integer. But these p-point formulas are not self-starting either. A rational method is established herein which will make these p-point formulas, and consequently also the multistep methods, self-starting. Subsequently the method is extended to systems of differential equations. (Author).

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.

Self-starting Multistep Methods for the Numerical Integration of Ordinary Differential Equations

Author : William A. Mersman
Publisher :
ISBN 13 :
Total Pages : 36 pages
Book Rating : 4.:/5 (31 download)

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Book Synopsis Self-starting Multistep Methods for the Numerical Integration of Ordinary Differential Equations by : William A. Mersman

Download or read book Self-starting Multistep Methods for the Numerical Integration of Ordinary Differential Equations written by William A. Mersman and published by . This book was released on 1965 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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.

Self-starting Multistep Methods for the Numerical Integration of Ordinary Differential Equations

Author : William A. Mersman
Publisher :
ISBN 13 :
Total Pages : 62 pages
Book Rating : 4.:/5 (249 download)

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Book Synopsis Self-starting Multistep Methods for the Numerical Integration of Ordinary Differential Equations by : William A. Mersman

Download or read book Self-starting Multistep Methods for the Numerical Integration of Ordinary Differential Equations written by William A. Mersman and published by . This book was released on 1965 with total page 62 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Modern Numerical Methods for Ordinary Differential Equations

Author : G. Hall
Publisher : Oxford University Press, USA
ISBN 13 :
Total Pages : 358 pages
Book Rating : 4.:/5 (44 download)

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Book Synopsis Modern Numerical Methods for Ordinary Differential Equations by : G. Hall

Download or read book Modern Numerical Methods for Ordinary Differential Equations written by G. Hall and published by Oxford University Press, USA. This book was released on 1976 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Numerical Methods for Differential Equations and Applications

Author : Liviu Gr. Ixaru
Publisher : Springer
ISBN 13 : 9789027715975
Total Pages : 364 pages
Book Rating : 4.7/5 (159 download)

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Book Synopsis Numerical Methods for Differential Equations and Applications by : Liviu Gr. Ixaru

Download or read book Numerical Methods for Differential Equations and Applications written by Liviu Gr. Ixaru and published by Springer. This book was released on 1984-08-31 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Solving Differential Equations by Multistep Initial and Boundary Value Methods

Author : L Brugnano
Publisher : CRC Press
ISBN 13 : 9789056991074
Total Pages : 438 pages
Book Rating : 4.9/5 (91 download)

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Book Synopsis Solving Differential Equations by Multistep Initial and Boundary Value Methods by : L Brugnano

Download or read book Solving Differential Equations by Multistep Initial and Boundary Value Methods written by L Brugnano and published by CRC Press. This book was released on 1998-05-22 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: The numerical approximation of solutions of differential equations has been, and continues to be, one of the principal concerns of numerical analysis and is an active area of research. The new generation of parallel computers have provoked a reconsideration of numerical methods. This book aims to generalize classical multistep methods for both initial and boundary value problems; to present a self-contained theory which embraces and generalizes the classical Dahlquist theory; to treat nonclassical problems, such as Hamiltonian problems and the mesh selection; and to select appropriate methods for a general purpose software capable of solving a wide range of problems efficiently, even on parallel computers.

Numerical Methods for Differential Equations

Author : J.R. Dormand
Publisher : CRC Press
ISBN 13 : 1351092006
Total Pages : 349 pages
Book Rating : 4.3/5 (51 download)

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Book Synopsis Numerical Methods for Differential Equations by : J.R. Dormand

Download or read book Numerical Methods for Differential Equations written by J.R. Dormand and published by CRC Press. This book was released on 2018-05-04 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: With emphasis on modern techniques, Numerical Methods for Differential Equations: A Computational Approach covers the development and application of methods for the numerical solution of ordinary differential equations. Some of the methods are extended to cover partial differential equations. All techniques covered in the text are on a program disk included with the book, and are written in Fortran 90. These programs are ideal for students, researchers, and practitioners because they allow for straightforward application of the numerical methods described in the text. The code is easily modified to solve new systems of equations. Numerical Methods for Differential Equations: A Computational Approach also contains a reliable and inexpensive global error code for those interested in global error estimation. This is a valuable text for students, who will find the derivations of the numerical methods extremely helpful and the programs themselves easy to use. It is also an excellent reference and source of software for researchers and practitioners who need computer solutions to differential equations.

Numerical Solution of Ordinary Differential Equations

Author : L. Fox
Publisher : Springer Science & Business Media
ISBN 13 : 9400931298
Total Pages : 259 pages
Book Rating : 4.4/5 (9 download)

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

Download or read book Numerical Solution of Ordinary Differential Equations written by L. Fox and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nearly 20 years ago we produced a treatise (of about the same length as this book) entitled Computing methods for scientists and engineers. It was stated that most computation is performed by workers whose mathematical training stopped somewhere short of the 'professional' level, and that some books are therefore needed which use quite simple mathematics but which nevertheless communicate the essence of the 'numerical sense' which is exhibited by the real computing experts and which is surely needed, at least to some extent, by all who use modern computers and modern numerical software. In that book we treated, at no great length, a variety of computational problems in which the material on ordinary differential equations occupied about 50 pages. At that time it was quite common to find books on numerical analysis, with a little on each topic ofthat field, whereas today we are more likely to see similarly-sized books on each major topic: for example on numerical linear algebra, numerical approximation, numerical solution ofordinary differential equations, numerical solution of partial differential equations, and so on. These are needed because our numerical education and software have improved and because our relevant problems exhibit more variety and more difficulty. Ordinary differential equa tions are obvious candidates for such treatment, and the current book is written in this sense.

Numerical Methods for Ordinary Differential Equations

Author : David Griffiths
Publisher : Springer
ISBN 13 : 9780857291479
Total Pages : 271 pages
Book Rating : 4.2/5 (914 download)

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Book Synopsis Numerical Methods for Ordinary Differential Equations by : David Griffiths

Download or read book Numerical Methods for Ordinary Differential Equations written by David Griffiths and published by Springer. This book was released on 2010-11-25 with total page 271 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

Scientific and Technical Aerospace Reports

Author :
Publisher :
ISBN 13 :
Total Pages : 1148 pages
Book Rating : 4.:/5 (31 download)

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Book Synopsis Scientific and Technical Aerospace Reports by :

Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1985 with total page 1148 pages. Available in PDF, EPUB and Kindle. Book excerpt:

U. S. Government Research and Development Reports

Author :
Publisher :
ISBN 13 :
Total Pages : 1776 pages
Book Rating : 4.:/5 (319 download)

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Book Synopsis U. S. Government Research and Development Reports by :

Download or read book U. S. Government Research and Development Reports written by and published by . This book was released on 1965 with total page 1776 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Technical Abstract Bulletin

Author :
Publisher :
ISBN 13 :
Total Pages : 908 pages
Book Rating : 4.E/5 ( download)

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Book Synopsis Technical Abstract Bulletin by :

Download or read book Technical Abstract Bulletin written by and published by . This book was released on with total page 908 pages. Available in PDF, EPUB and Kindle. Book excerpt:

General Linear Methods for Ordinary Differential Equations

Author : Zdzislaw Jackiewicz
Publisher : John Wiley & Sons
ISBN 13 : 0470522151
Total Pages : 500 pages
Book Rating : 4.4/5 (75 download)

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Book Synopsis General Linear Methods for Ordinary Differential Equations by : Zdzislaw Jackiewicz

Download or read book General Linear Methods for Ordinary Differential Equations written by Zdzislaw Jackiewicz and published by John Wiley & Sons. This book was released on 2009-08-14 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

A Variable Order Multistep Method for the Numerical Solution of Stift Systems of Ordinary Differential Equations

Author : J. A. I. Craigie
Publisher :
ISBN 13 :
Total Pages : 67 pages
Book Rating : 4.:/5 (897 download)

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Book Synopsis A Variable Order Multistep Method for the Numerical Solution of Stift Systems of Ordinary Differential Equations by : J. A. I. Craigie

Download or read book A Variable Order Multistep Method for the Numerical Solution of Stift Systems of Ordinary Differential Equations written by J. A. I. Craigie and published by . This book was released on 1975 with total page 67 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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.