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Author : I. Gladwell,D. K. Sayers,Institute of Mathematics and Its Applications
Publisher : Unknown
Page : 328 pages
File Size : 47,5 Mb
Release : 1980
Category : Differential equations
ISBN : UCAL:B5008559
Author : I. Gladwell
Publisher : Unknown
Page : 304 pages
File Size : 40,9 Mb
Release : 1980
Category : Differential equations
ISBN : OCLC:1046445340
Author : J. D. Lambert
Publisher : Unknown
Page : 278 pages
File Size : 53,9 Mb
Release : 1983
Category : Electronic
ISBN : OCLC:1024537503
Author : Kenneth Eriksson
Publisher : Cambridge University Press
Page : 558 pages
File Size : 51,8 Mb
Release : 1996-09-05
Category : Mathematics
ISBN : 0521567386
This textbook on computational mathematics is based on a fusion of mathematical analysis, numerical computation and applications.
Author : J. Noye
Publisher : Elsevier
Page : 678 pages
File Size : 52,8 Mb
Release : 2000-04-01
Category : Mathematics
ISBN : 0080871941
Computational Techniques for Differential Equations
Author : J.R. Dormand
Publisher : CRC Press
Page : 385 pages
File Size : 54,6 Mb
Release : 2018-05-04
Category : Mathematics
ISBN : 9781351083553
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.
Author : John Denholm Lambert
Publisher : Unknown
Page : 306 pages
File Size : 47,9 Mb
Release : 1973-02-16
Category : Mathematics
ISBN : UOM:39015049310520
Author : Jack D. Lambert
Publisher : Unknown
Page : 128 pages
File Size : 46,6 Mb
Release : 1974
Category : Electronic
ISBN : OCLC:615111419
Author : David F. Griffiths,Desmond J. Higham
Publisher : Springer Science & Business Media
Page : 271 pages
File Size : 45,6 Mb
Release : 2010-11-11
Category : Mathematics
ISBN : 9780857291486
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
Author : Uri M. Ascher,Linda R. Petzold
Publisher : SIAM
Page : 305 pages
File Size : 50,7 Mb
Release : 1998-01-01
Category : Mathematics
ISBN : 161197139X
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.
Author : Uri M. Ascher
Publisher : SIAM
Page : 403 pages
File Size : 47,6 Mb
Release : 2008-09-04
Category : Mathematics
ISBN : 9780898716528
Develops, analyses, and applies numerical methods for evolutionary, or time-dependent, differential problems.
Author : J. D. Lambert
Publisher : Wiley-Blackwell
Page : 293 pages
File Size : 53,5 Mb
Release : 1991
Category : Mathematics
ISBN : 0471929905
Numerical Methods for Ordinary Differential Systems The Initial Value Problem J. D. Lambert Professor of Numerical Analysis University of Dundee Scotland In 1973 the author published a book entitled Computational Methods in Ordinary Differential Equations. Since then, there have been many new developments in this subject and the emphasis has changed substantially. This book reflects these changes; it is intended not as a revision of the earlier work but as a complete replacement for it. Although some basic material appears in both books, the treatment given here is generally different and there is very little overlap. In 1973 there were many methods competing for attention but more recently there has been increasing emphasis on just a few classes of methods for which sophisticated implementations now exist. This book places much more emphasis on such implementations—and on the important topic of stiffness—than did its predecessor. Also included are accounts of the structure of variable-step, variable-order methods, the Butcher and the Albrecht theories for Runge—Kutta methods, order stars and nonlinear stability theory. The author has taken a middle road between analytical rigour and a purely computational approach, key results being stated as theorems but proofs being provided only where they aid the reader’s understanding of the result. Numerous exercises, from the straightforward to the demanding, are included in the text. This book will appeal to advanced students and teachers of numerical analysis and to users of numerical methods who wish to understand how algorithms for ordinary differential systems work and, on occasion, fail to work.
Author : J. C. Butcher
Publisher : John Wiley & Sons
Page : 546 pages
File Size : 50,6 Mb
Release : 2016-08-29
Category : Mathematics
ISBN : 9781119121503
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.
Author : Peter Deuflhard,Folkmar Bornemann
Publisher : Springer Science & Business Media
Page : 498 pages
File Size : 40,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9780387215822
Well-known authors; Includes topics and results that have previously not been covered in a book; Uses many interesting examples from science and engineering; Contains numerous homework exercises; Scientific computing is a hot and topical area
Author : Anonim
Publisher : Academic Press
Page : 322 pages
File Size : 46,9 Mb
Release : 1971-03-31
Category : Mathematics
ISBN : 0080955835
In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation; methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; and methods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory. As a result, the book represents a blend of new methods in general computational analysis, and specific, but also generic, techniques for study of systems theory ant its particular branches, such as optimal filtering and information compression. - Best operator approximation, - Non-Lagrange interpolation, - Generic Karhunen-Loeve transform - Generalised low-rank matrix approximation - Optimal data compression - Optimal nonlinear filtering