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Author : Kenneth Eriksson
Publisher : Cambridge University Press
Page : 558 pages
File Size : 55,8 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 : Peter Deuflhard,Folkmar Bornemann
Publisher : Springer Science & Business Media
Page : 498 pages
File Size : 45,8 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 : Charles E. Roberts
Publisher : Prentice Hall
Page : 432 pages
File Size : 48,5 Mb
Release : 1979
Category : Mathematics
ISBN : UOM:39015004689231
Author : Ernst Hairer,Syvert P. Nørsett,Gerhard Wanner
Publisher : Springer Science & Business Media
Page : 541 pages
File Size : 49,8 Mb
Release : 2008-04-03
Category : Mathematics
ISBN : 9783540788621
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.
Author : J.R. Dormand
Publisher : CRC Press
Page : 283 pages
File Size : 46,6 Mb
Release : 2018-05-04
Category : Mathematics
ISBN : 9781351092005
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 : Richard S. Palais,Robert Andrew Palais
Publisher : American Mathematical Soc.
Page : 329 pages
File Size : 54,8 Mb
Release : 2009-11-13
Category : Mathematics
ISBN : 9780821821381
This book provides a conceptual introduction to the theory of ordinary differential equations, concentrating on the initial value problem for equations of evolution and with applications to the calculus of variations and classical mechanics, along with a discussion of chaos theory and ecological models. It has a unified and visual introduction to the theory of numerical methods and a novel approach to the analysis of errors and stability of various numerical solution algorithms based on carefully chosen model problems. While the book would be suitable as a textbook for an undergraduate or elementary graduate course in ordinary differential equations, the authors have designed the text also to be useful for motivated students wishing to learn the material on their own or desiring to supplement an ODE textbook being used in a course they are taking with a text offering a more conceptual approach to the subject.
Author : I. Gladwell,D. K. Sayers,Institute of Mathematics and Its Applications
Publisher : Unknown
Page : 328 pages
File Size : 48,5 Mb
Release : 1980
Category : Differential equations
ISBN : UCAL:B5008559
Author : Uri M. Ascher
Publisher : SIAM
Page : 403 pages
File Size : 53,8 Mb
Release : 2008-09-04
Category : Mathematics
ISBN : 9780898716528
Develops, analyses, and applies numerical methods for evolutionary, or time-dependent, differential problems.
Author : David F. Griffiths,Desmond J. Higham
Publisher : Springer Science & Business Media
Page : 271 pages
File Size : 51,9 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 : Charles Roberts
Publisher : CRC Press
Page : 604 pages
File Size : 40,8 Mb
Release : 2011-06-13
Category : Mathematics
ISBN : 9781439819098
In the traditional curriculum, students rarely study nonlinear differential equations and nonlinear systems due to the difficulty or impossibility of computing explicit solutions manually. Although the theory associated with nonlinear systems is advanced, generating a numerical solution with a computer and interpreting that solution are fairly elementary. Bringing the computer into the classroom, Ordinary Differential Equations: Applications, Models, and Computing emphasizes the use of computer software in teaching differential equations. Providing an even balance between theory, computer solution, and application, the text discusses the theorems and applications of the first-order initial value problem, including learning theory models, population growth models, epidemic models, and chemical reactions. It then examines the theory for n-th order linear differential equations and the Laplace transform and its properties, before addressing several linear differential equations with constant coefficients that arise in physical and electrical systems. The author also presents systems of first-order differential equations as well as linear systems with constant coefficients that arise in physical systems, such as coupled spring-mass systems, pendulum systems, the path of an electron, and mixture problems. The final chapter introduces techniques for determining the behavior of solutions to systems of first-order differential equations without first finding the solutions. Designed to be independent of any particular software package, the book includes a CD-ROM with the software used to generate the solutions and graphs for the examples. The appendices contain complete instructions for running the software. A solutions manual is available for qualifying instructors.
Author : Gene H. Golub,James M. Ortega
Publisher : Academic Press
Page : 360 pages
File Size : 49,9 Mb
Release : 1992
Category : Computers
ISBN : 0122892550
A book that emphasizes the importance of solving differential equations on a computer, which comprises a large part of what has come to be called scientific computing. An introductory chapter on this topic gives an overview of modern scientific computing, outlining its applications and placing the subject in a larger context.
Author : Jack D. Lambert
Publisher : Unknown
Page : 128 pages
File Size : 49,5 Mb
Release : 1974
Category : Electronic
ISBN : OCLC:615111419
Author : John Denholm Lambert
Publisher : Unknown
Page : 306 pages
File Size : 44,7 Mb
Release : 1973-02-16
Category : Mathematics
ISBN : UOM:39015049310520
Author : Institute of Mathematics and Its Applications
Publisher : Oxford University Press, USA
Page : 488 pages
File Size : 45,5 Mb
Release : 1992
Category : Differential equations
ISBN : UCAL:B4405916
This collection of refereed papers from an international conference provides a comprehensive coverage of recent research on the numerical solution of ordinary differential equations. There are sections on initial value problems, boundary value problems, differential algebraic equations,applications to the solution of partial differential equations, parallel solution methods, and methods of conservation and global error calculation. Within each section the papers have been ordered so that the reader will perceive a gradual movement from the theoretical to the practical. Newchallenges such as the solution of differential-algebraic equations and the impact of parallelism are covered alongside currently topical aspects of older problems such as the interpolation of Runge-Kutta methods and the development of formulas which conserve energy whilst preserving accuracy. Fornumerical analysts in academic and industrial research this book provides detailed coverage of this important subject.
Author : Simeon Ola Fatunla
Publisher : Unknown
Page : 308 pages
File Size : 42,6 Mb
Release : 1992
Category : Differential equations
ISBN : 978249321X