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Multirate Linear Multistep Methods For The Solution Of Systems Of Ordinary Differential Equations
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Book Synopsis Multirate Linear Multistep Methods for the Solution of Systems of Ordinary Differential Equations by : Daniel R. Wells
Download or read book Multirate Linear Multistep Methods for the Solution of Systems of Ordinary Differential Equations written by Daniel R. Wells and published by . This book was released on 1982 with total page 106 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 2008-04-15 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years the study of numerical methods for solving ordinary differential equations has seen many new developments. This second edition of the author's pioneering text is fully revised and updated to acknowledge many of these developments. It includes a complete treatment of linear multistep methods whilst maintaining its unique and comprehensive emphasis on Runge-Kutta methods and general linear methods. Although the specialist topics are taken to an advanced level, the entry point to the volume as a whole is not especially demanding. Early chapters provide a wide-ranging introduction to differential equations and difference equations together with a survey of numerical differential equation methods, based on the fundamental Euler method with more sophisticated methods presented as generalizations of Euler. Features of the book include Introductory work on differential and difference equations. A comprehensive introduction to the theory and practice of solving ordinary differential equations numerically. A detailed analysis of Runge-Kutta methods and of linear multistep methods. A complete study of general linear methods from both theoretical and practical points of view. The latest results on practical general linear methods and their implementation. A balance between informal discussion and rigorous mathematical style. Examples and exercises integrated into each chapter enhancing the suitability of the book as a course text or a self-study treatise. Written in a lucid style by one of the worlds leading authorities on numerical methods for ordinary differential equations and drawing upon his vast experience, this new edition provides an accessible and self-contained introduction, ideal for researchers and students following courses on numerical methods, engineering and other sciences.
Book Synopsis Numerical Solution of Ordinary Differential Equations by :
Download or read book Numerical Solution of Ordinary Differential Equations written by and published by Academic Press. This book was released on 1971-03-31 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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; andmethods 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 particularbranches, 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
Book Synopsis Automatic Multirate Methods for Ordinary Differential Equations by : Charles William Gear
Download or read book Automatic Multirate Methods for Ordinary Differential Equations written by Charles William Gear and published by . This book was released on 1980 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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. This book was released on 2010-03-10 with total page 627 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of this book is the solution of stiff differential equations and of differential-algebraic systems. This second edition contains new material including new numerical tests, recent progress in numerical differential-algebraic equations, and improved FORTRAN codes. From the reviews: "A superb book...Throughout, illuminating graphics, sketches and quotes from papers of researchers in the field add an element of easy informality and motivate the text." --MATHEMATICS TODAY
Book Synopsis On Modified Optimal Linear Multistep Methods for Systems of Ordinary Differential Equations by : Godelieve Tilquin
Download or read book On Modified Optimal Linear Multistep Methods for Systems of Ordinary Differential Equations written by Godelieve Tilquin and published by . This book was released on 1971 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Multirate Integration Methods. The Numerical Solution of Stiff Systems of Ordinary Differential Equations by Multirate Integration Methods by : S. Skelboe
Download or read book Multirate Integration Methods. The Numerical Solution of Stiff Systems of Ordinary Differential Equations by Multirate Integration Methods written by S. Skelboe and published by . This book was released on 1984 with total page 64 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 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.
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. This book was released on 1987 with total page 632 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.
Book Synopsis Multi-derivative Numerical Methods for the Solution of Stiff Ordinary Differential Equations by : Roy Leonard Brown
Download or read book Multi-derivative Numerical Methods for the Solution of Stiff Ordinary Differential Equations written by Roy Leonard Brown and published by . This book was released on 1975 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Scientific and Technical Aerospace Reports by :
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1983 with total page 1252 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A New Theory for Multistep Discretizations of Stiff Ordinary Differential Equations: Stability with Large Step Sizes by : George Majda
Download or read book A New Theory for Multistep Discretizations of Stiff Ordinary Differential Equations: Stability with Large Step Sizes written by George Majda and published by . This book was released on 1985 with total page 76 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 36 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 Nonlinear Multistep Methods for Solving Initial Value Problems in Ordinary Differential Equations by : Ding Lee
Download or read book Nonlinear Multistep Methods for Solving Initial Value Problems in Ordinary Differential Equations written by Ding Lee and published by . This book was released on 1974 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: The report develops a family of Nonlinear Multistep (NLMS) numerical methods which solve initial value problems for systems of first-order differential equations. These methods are demonstrated to be a generalization of Linear Multistep (LMS) methods and are formulated to be particularly effective for equations whose solutions are asymptotically stable. The formal theory of NLMS methods with regard to stability, consistency, and convergence is fully developed and proved. NLMS methods are strongly stable and accommodate A-stability in the sense of Dahlquist. Extensive numerical test results produced by NLMS methods show important advantages over Adams' and Gear's methods and Ehle's test results. (Author).
