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Author : W. H. Hundsdorfer
Publisher :
ISBN 13 :
Total Pages : 158 pages
Book Rating : 4.:/5 (44 download)
Download or read book The Numerical Solution of Nonlinear Stiff Initial Value Problems written by W. H. Hundsdorfer and published by . This book was released on 1985 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : W. H. Hundsdorfer
Publisher :
ISBN 13 :
Total Pages : 138 pages
Book Rating : 4.:/5 (144 download)
Download or read book The Numerical Solution of Nonlinear Stiff Initial Value Problems written by W. H. Hundsdorfer and published by . This book was released on 1985 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :
Publisher :
ISBN 13 :
Total Pages : 44 pages
Book Rating : 4.:/5 (317 download)
Download or read book Numerical Solutions of Nonlinear STIFF Initial Value Problems by Perturbed Functional Iterations written by and published by . This book was released on 1982 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Simeon Ola Fatunla
Publisher : Academic Press
ISBN 13 : 1483269264
Total Pages : 308 pages
Book Rating : 4.4/5 (832 download)
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.
Author : K. E. Brenan
Publisher : SIAM
ISBN 13 : 0898713536
Total Pages : 261 pages
Book Rating : 4.8/5 (987 download)
Download or read book Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations written by K. E. Brenan and published by SIAM. This book was released on 1996-01-01 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes some of the places where differential-algebraic equations (DAE's) occur.
Author : A.K. Aziz
Publisher : Academic Press
ISBN 13 : 1483267997
Total Pages : 380 pages
Book Rating : 4.4/5 (832 download)
Download or read book Numerical Solutions of Boundary Value Problems for Ordinary Differential Equations written by A.K. Aziz and published by Academic Press. This book was released on 2014-05-10 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical Solutions of Boundary Value Problems for Ordinary Differential Equations covers the proceedings of the 1974 Symposium by the same title, held at the University of Maryland, Baltimore Country Campus. This symposium aims to bring together a number of numerical analysis involved in research in both theoretical and practical aspects of this field. This text is organized into three parts encompassing 15 chapters. Part I reviews the initial and boundary value problems. Part II explores a large number of important results of both theoretical and practical nature of the field, including discussions of the smooth and local interpolant with small K-th derivative, the occurrence and solution of boundary value reaction systems, the posteriori error estimates, and boundary problem solvers for first order systems based on deferred corrections. Part III highlights the practical applications of the boundary value problems, specifically a high-order finite-difference method for the solution of two-point boundary-value problems on a uniform mesh. This book will prove useful to mathematicians, engineers, and physicists.
Author : S. K. Dey
Publisher :
ISBN 13 :
Total Pages : 35 pages
Book Rating : 4.:/5 (167 download)
Download or read book Numerical Solution of Nonlinear STIFF Initial-value Problems by Perturbed Functional Iterations written by S. K. Dey and published by . This book was released on 1982 with total page 35 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Uri M. Ascher
Publisher : SIAM
ISBN 13 : 0898713544
Total Pages : 617 pages
Book Rating : 4.8/5 (987 download)
Download or read book Numerical Solution of Boundary Value Problems for Ordinary Differential Equations written by Uri M. Ascher and published by SIAM. This book was released on 1988-01-01 with total page 617 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the most comprehensive, up-to-date account of the popular numerical methods for solving boundary value problems in ordinary differential equations. It aims at a thorough understanding of the field by giving an in-depth analysis of the numerical methods by using decoupling principles. Numerous exercises and real-world examples are used throughout to demonstrate the methods and the theory. Although first published in 1988, this republication remains the most comprehensive theoretical coverage of the subject matter, not available elsewhere in one volume. Many problems, arising in a wide variety of application areas, give rise to mathematical models which form boundary value problems for ordinary differential equations. These problems rarely have a closed form solution, and computer simulation is typically used to obtain their approximate solution. This book discusses methods to carry out such computer simulations in a robust, efficient, and reliable manner.
Author : Kendall Atkinson
Publisher : John Wiley & Sons
ISBN 13 : 1118164520
Total Pages : 272 pages
Book Rating : 4.1/5 (181 download)
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.
Author : David F. Griffiths
Publisher : Springer Science & Business Media
ISBN 13 : 0857291483
Total Pages : 274 pages
Book Rating : 4.8/5 (572 download)
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
Author : G. Hall
Publisher : Oxford University Press, USA
ISBN 13 :
Total Pages : 358 pages
Book Rating : 4.:/5 (44 download)
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:
Author : Christopher T. H. Baker
Publisher : Oxford University Press, USA
ISBN 13 :
Total Pages : 394 pages
Book Rating : 4.F/5 ( download)
Download or read book The Numerical Solution of Nonlinear Problems written by Christopher T. H. Baker and published by Oxford University Press, USA. This book was released on 1981 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Ralph Willoughby
Publisher : Springer Science & Business Media
ISBN 13 : 146842100X
Total Pages : 324 pages
Book Rating : 4.4/5 (684 download)
Download or read book Stiff Differential Systems written by Ralph Willoughby and published by Springer Science & Business Media. This book was released on 2013-03-13 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: The papers in these proceedings were presented at an Inter national Symposium on Stiff Differential Systems, which was held at the Hotel Quellenhof, Wildbad, Federal Republic of Germany, October 4-6, 1973. The sumposium was organized by IBM Germany and sponsored by the IBM World Trade Corporation. On behalf of all the participants we wish to express our appreciation to the sponsors and organizers for their generous support,particularly to Dr. G. HUbner, representing Scientific Relations, IBM Germany, and Dr. G. Kozak, representing IBM World Trade Headquarters, New York. The purpose of the conference was to provide an intensive treatment of all apsects of a difficult problem class, stiff differential systems. Some major fields of interest of attendees and contributors are: 1) Modeling and problem solving in scien tific and technological applications, 2) Qualitative theory of stiff systems, 3) Numerical Analysis, including design, valida tion, and comparison of algorithms, as well as error and stability analysis, and 4) Computer Science, in particular problem-oriented programming languages, program packages, and applications-oriented computer architecture.
Author : Milan Kubicek
Publisher : Courier Corporation
ISBN 13 : 0486463001
Total Pages : 338 pages
Book Rating : 4.4/5 (864 download)
Download or read book Numerical Solution of Nonlinear Boundary Value Problems with Applications written by Milan Kubicek and published by Courier Corporation. This book was released on 2008-01-01 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: A survey of the development, analysis, and application of numerical techniques in solving nonlinear boundary value problems, this text presents numerical analysis as a working tool for physicists and engineers. Starting with a survey of accomplishments in the field, it explores initial and boundary value problems for ordinary differential equations, linear boundary value problems, and the numerical realization of parametric studies in nonlinear boundary value problems. The authors--Milan Kubicek, Professor at the Prague Institute of Chemical Technology, and Vladimir Hlavacek, Professor at the University of Buffalo--emphasize the description and straightforward application of numerical techniques rather than underlying theory. This approach reflects their extensive experience with the application of diverse numerical algorithms.
Author : Ülo Lepik
Publisher : Springer Science & Business Media
ISBN 13 : 3319042955
Total Pages : 209 pages
Book Rating : 4.3/5 (19 download)
Download or read book Haar Wavelets written by Ülo Lepik and published by Springer Science & Business Media. This book was released on 2014-01-09 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book to present a systematic review of applications of the Haar wavelet method for solving Calculus and Structural Mechanics problems. Haar wavelet-based solutions for a wide range of problems, such as various differential and integral equations, fractional equations, optimal control theory, buckling, bending and vibrations of elastic beams are considered. Numerical examples demonstrating the efficiency and accuracy of the Haar method are provided for all solutions.
Author : Granville Sewell
Publisher : Academic Press
ISBN 13 : 1483259145
Total Pages : 284 pages
Book Rating : 4.4/5 (832 download)
Download or read book The Numerical Solution of Ordinary and Partial Differential Equations written by Granville Sewell and published by Academic Press. This book was released on 2014-05-10 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Numerical Solution of Ordinary and Partial Differential Equations is an introduction to the numerical solution of ordinary and partial differential equations. Finite difference methods for solving partial differential equations are mostly classical low order formulas, easy to program but not ideal for problems with poorly behaved solutions or (especially) for problems in irregular multidimensional regions. FORTRAN77 programs are used to implement many of the methods studied. Comprised of six chapters, this book begins with a review of direct methods for the solution of linear systems, with emphasis on the special features of the linear systems that arise when differential equations are solved. The next four chapters deal with the more commonly used finite difference methods for solving a variety of problems, including both ordinary differential equations and partial differential equations, and both initial value and boundary value problems. The final chapter is an overview of the basic ideas behind the finite element method and covers the Galerkin method for boundary value problems. Examples using piecewise linear trial functions, cubic hermite trial functions, and triangular elements are presented. This monograph is appropriate for senior-level undergraduate or first-year graduate students of mathematics.
Author : Ernst Hairer
Publisher : Springer Science & Business Media
ISBN 13 : 3662126079
Total Pages : 491 pages
Book Rating : 4.6/5 (621 download)
Download or read book Solving Ordinary Differential Equations I written by Ernst Hairer and published by Springer Science & Business Media. This book was released on 2013-11-27 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: "So far as I remember, I have never seen an Author's Pre face which had any purpose but one - to furnish reasons for the publication of the Book. " (Mark Twain) "Gauss' dictum, "when a building is completed no one should be able to see any trace of the scaffolding," is often used by mathematicians as an excuse for neglecting the motivation behind their own work and the history of their field. For tunately, the opposite sentiment is gaining strength, and numerous asides in this Essay show to which side go my sympathies. " (B. B. Mandelbrot, 1982) 'This gives us a good occasion to work out most of the book until the next year. " (the Authors in a letter, dated c. kt. 29, 1980, to Springer Verlag) There are two volumes, one on non-stiff equations, now finished, the second on stiff equations, in preparation. The first volume has three chapters, one on classical mathematical theory, one on Runge Kutta and extrapolation methods, and one on multistep methods. There is an Appendix containing some Fortran codes which we have written for our numerical examples. Each chapter is divided into sections. Numbers of formulas, theorems, tables and figures are consecutive in each section and indi cate, in addition, the section number, but not the chapter number. Cross references to other chapters are rare and are stated explicitly. The end of a proof is denoted by "QED" (quod erat demonstrandum).
