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Self Starting Multistep Methods For The Numerical Integration Of Ordinary Differential Equations
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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:
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:
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.
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).
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.
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
Book Synopsis Stability of Multistep Methods in Numerical Integration by : Robert Nelson Lea
Download or read book Stability of Multistep Methods in Numerical Integration written by Robert Nelson Lea and published by . This book was released on 1965 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis An Explicit Modified Multistep Method for the Numerical Integration of Ordinary Differential Equations by : Millard T. Hardrider
Download or read book An Explicit Modified Multistep Method for the Numerical Integration of Ordinary Differential Equations written by Millard T. Hardrider and published by . This book was released on 1966 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Geometric Numerical Integration by : Ernst Hairer
Download or read book Geometric Numerical Integration written by Ernst Hairer and published by Springer Science & Business Media. This book was released on 2006-05-18 with total page 660 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers numerical methods that preserve properties of Hamiltonian systems, reversible systems, differential equations on manifolds and problems with highly oscillatory solutions. It presents a theory of symplectic and symmetric methods, which include various specially designed integrators, as well as discusses their construction and practical merits. The long-time behavior of the numerical solutions is studied using a backward error analysis combined with KAM theory.
Book Synopsis An Operational Unification of Finite Difference Methods for the Numerical Integration of Ordinary Differential Equations by : Harvard Lomax
Download or read book An Operational Unification of Finite Difference Methods for the Numerical Integration of Ordinary Differential Equations written by Harvard Lomax and published by . This book was released on 1967 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: One purpose of this report is to present a mathematical procedure which can be used to study and compare various numerical methods for integrating ordinary differential equations. This procedure is relatively simple, mathematically rigorous, and of such a nature that matters of interest in digital computations, such as machine memory and running time, can be weighed against the accuracy and stability provided by the method under consideration. Briefly, the procedure is as follows: (1) Find a single differential equation that is sufficiently representative (this is fully defined in the report) of an arbitrary number of nonhomogeneous, linear, ordinary differential equations with constant coefficients. (2) Solve this differential equation exactly. (3) Choose any given numerical method, use it -- in its entirety -- to reduce the differential equation to difference equations, and, by means of operational techniques, solve the latter exactly. (4) Study and compare the results of (2) and (3). Conceptually there is nothing new in this procedure, but the particular development presented in this report does not appear to have been carried out before. Another purpose is to use the procedure just described to analyze a variety of numerical methods, ranging from classical, predictor-corrector systems to Runge-Kutta techniques and including various combinations of the two.
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.
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:
Book Synopsis The Numerical Integration of Ordinary, Differential Equations by : T. E. Hull
Download or read book The Numerical Integration of Ordinary, Differential Equations written by T. E. Hull and published by . This book was released on 1966 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book NASA Technical Note written by and published by . This book was released on 1965 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Book Synopsis Numerical Solution of Initial Value Problems by : Francis Ceschino
Download or read book Numerical Solution of Initial Value Problems written by Francis Ceschino and published by . This book was released on 1966 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction -- Part 1 : The single-step methods -- Generalities on the single-step methods Euler's method-Taylor's series -- Runge-Kutta method -- Relationships of the Runge-Kutta principle with the various single-step methods -- Runge-Kutta type formulas using higher order derivatives -- Part 2 : Multistep methods -- Adams method and analogues -- Different multistep formulas -- Application of the Runge-Kutta principle to the multistep methods -- Part 3 : Theoretical and practical considerations -- Theoretical considerations -- Practical considerations.
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:
