Numerical Methods for Initial Value Problems in Ordinary Differential Equations

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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.

Multistep Methods for Stiff Initial Value Problems

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Publisher :
ISBN 13 :
Total Pages : 196 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Multistep Methods for Stiff Initial Value Problems by : Dana Petcu

Download or read book Multistep Methods for Stiff Initial Value Problems written by Dana Petcu and published by . This book was released on 1995 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt:

A Nonlinear Multistep Method for Solving Stiff Initial Value Problems

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Publisher :
ISBN 13 :
Total Pages : 180 pages
Book Rating : 4.3/5 (129 download)

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Book Synopsis A Nonlinear Multistep Method for Solving Stiff Initial Value Problems by : Moody Ten-Chao Chu

Download or read book A Nonlinear Multistep Method for Solving Stiff Initial Value Problems written by Moody Ten-Chao Chu and published by . This book was released on 1982 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Solving Ordinary Differential Equations II

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Publisher : Springer Science & Business Media
ISBN 13 : 3662099470
Total Pages : 615 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Solving Ordinary Differential Equations II by : Ernst Hairer

Download or read book Solving Ordinary Differential Equations II written by Ernst Hairer and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 615 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Whatever regrets may be, we have done our best." (Sir Ernest Shackleton, turning back on 9 January 1909 at 88°23' South.) Brahms struggled for 20 years to write his first symphony. Compared to this, the 10 years we have been working on these two volumes may even appear short. This second volume treats stiff differential equations and differential alge braic equations. It contains three chapters: Chapter IV on one-step (Runge Kutta) methods for stiff problems, Chapter Von multistep methods for stiff problems, and Chapter VI on singular perturbation and differential-algebraic equations. Each chapter is divided into sections. Usually the first sections of a chapter are of an introductory nature, explain numerical phenomena and exhibit numerical results. Investigations of a more theoretieal nature are presented in the later sections of each chapter. As in Volume I, the formulas, theorems, tables and figures are numbered consecutively in each section and indicate, in addition, the section num ber. In cross references to other chapters the (latin) chapter number is put first. References to the bibliography are again by "author" plus "year" in parentheses. The bibliography again contains only those papers which are discussed in the text and is in no way meant to be complete.

Solving Differential Equations by Multistep Initial and Boundary Value Methods

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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.

Construction Of Integration Formulas For Initial Value Problems

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Publisher : Elsevier
ISBN 13 : 0444601899
Total Pages : 282 pages
Book Rating : 4.4/5 (446 download)

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Book Synopsis Construction Of Integration Formulas For Initial Value Problems by : P.J. Van Der Houwen

Download or read book Construction Of Integration Formulas For Initial Value Problems written by P.J. Van Der Houwen and published by Elsevier. This book was released on 2012-12-02 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: Construction of Integration Formulas for Initial Value Problems provides practice-oriented insights into the numerical integration of initial value problems for ordinary differential equations. It describes a number of integration techniques, including single-step methods such as Taylor methods, Runge-Kutta methods, and generalized Runge-Kutta methods. It also looks at multistep methods and stability polynomials. Comprised of four chapters, this volume begins with an overview of definitions of important concepts and theorems that are relevant to the construction of numerical integration methods for initial value problems. It then turns to a discussion of how to convert two-point and initial boundary value problems for partial differential equations into initial value problems for ordinary differential equations. The reader is also introduced to stiff differential equations, partial differential equations, matrix theory and functional analysis, and non-linear equations. The order of approximation of the single-step methods to the differential equation is considered, along with the convergence of a consistent single-step method. There is an explanation on how to construct integration formulas with adaptive stability functions and how to derive the most important stability polynomials. Finally, the book examines the consistency, convergence, and stability conditions for multistep methods. This book is a valuable resource for anyone who is acquainted with introductory calculus, linear algebra, and functional analysis.

Convergence of Linear Multistep and One-leg Methods for Stiff Nonlinear Initial Value Problems

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Publisher :
ISBN 13 :
Total Pages : 17 pages
Book Rating : 4.:/5 (222 download)

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Book Synopsis Convergence of Linear Multistep and One-leg Methods for Stiff Nonlinear Initial Value Problems by : W. H. Hundsdorfer

Download or read book Convergence of Linear Multistep and One-leg Methods for Stiff Nonlinear Initial Value Problems written by W. H. Hundsdorfer and published by . This book was released on 1989 with total page 17 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "To prove convergence of numerical methods for stiff initial value problems, stability is needed but also estimates for the local errors which are not affected by stiffness. In this paper global error bounds are derived for one-leg and linear multistep methods applied to classes of arbitrarily stiff, nonlinear initial value problems. It will be shown that under suitable stability assumptions the multistep methods are convergent for stiff problems with the same order of convergence as for nonstiff problems, provided that the stepsize variation is sufficiently regular."

Numerical Methods for Ordinary Differential Equations

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Publisher : Springer Science & Business Media
ISBN 13 : 0857291483
Total Pages : 274 pages
Book Rating : 4.8/5 (572 download)

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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

Numerical Methods for Ordinary Differential Equations

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Publisher : John Wiley & Sons
ISBN 13 : 1119121523
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 2016-08-05 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.

Multistep Multiderivative Methods for the Numerical Solution of Initial Value Problems of Ordinary Differential Equations

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Publisher :
ISBN 13 :
Total Pages : 352 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Multistep Multiderivative Methods for the Numerical Solution of Initial Value Problems of Ordinary Differential Equations by : Rolf Jeltsch

Download or read book Multistep Multiderivative Methods for the Numerical Solution of Initial Value Problems of Ordinary Differential Equations written by Rolf Jeltsch and published by . This book was released on 1976 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Convergence of One-leg Multistep Methods for Stiff Nonlinear Initial Value Problems

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Publisher :
ISBN 13 :
Total Pages : 14 pages
Book Rating : 4.:/5 (256 download)

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Book Synopsis Convergence of One-leg Multistep Methods for Stiff Nonlinear Initial Value Problems by : Willem H. Hundsdorfer

Download or read book Convergence of One-leg Multistep Methods for Stiff Nonlinear Initial Value Problems written by Willem H. Hundsdorfer and published by . This book was released on 1989 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Modern Numerical Methods for Ordinary Differential Equations

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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:

Convergence of One-leg Multistep Methods for Stiff Nonlinear Intial Value Problems

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Publisher :
ISBN 13 :
Total Pages : 14 pages
Book Rating : 4.:/5 (29 download)

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Book Synopsis Convergence of One-leg Multistep Methods for Stiff Nonlinear Intial Value Problems by : W. H. Hundsdorfer

Download or read book Convergence of One-leg Multistep Methods for Stiff Nonlinear Intial Value Problems written by W. H. Hundsdorfer and published by . This book was released on 1989 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "For proving convergence of numerical methods for stiff initial value problems, not only stability is needed, but also bounds for the local errors which are not affected by stiffness. In this paper global error bounds are derived for multistep schemes applied to classes of arbitrarily stiff, nonlinear initial value problems. It will be shown that stable one-leg methods are convergent for stiff problems with the same order as for nonstiff problems, provided that the stepsize variation is sufficiently regular. Using a well known equivalence relation between one-leg and linear multistep methods, convergence results for linear multistep methods on uniform grids will also be obtained."

Stiff Differential Systems

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Publisher : Springer Science & Business Media
ISBN 13 : 146842100X
Total Pages : 324 pages
Book Rating : 4.4/5 (684 download)

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Book Synopsis Stiff Differential Systems by : Ralph Willoughby

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.

Modified Linear Multistep Methods for the Numerical Integration of Stiff Initial Value Problems

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Publisher :
ISBN 13 :
Total Pages : 472 pages
Book Rating : 4.:/5 (94 download)

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Book Synopsis Modified Linear Multistep Methods for the Numerical Integration of Stiff Initial Value Problems by : Seamus Considine

Download or read book Modified Linear Multistep Methods for the Numerical Integration of Stiff Initial Value Problems written by Seamus Considine and published by . This book was released on 1988 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Numerical Solution of Ordinary Differential Equations

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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.

Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations

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Publisher : SIAM
ISBN 13 : 0898713536
Total Pages : 261 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations by : K. E. Brenan

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.