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Author : Charles William Gear
Publisher :
ISBN 13 :
Total Pages : 30 pages
Book Rating : 4.:/5 (31 download)
Download or read book Stability of Variable-step Methods for Ordinary Differential Equations written by Charles William Gear and published by . This book was released on 1978 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Zdzislaw Jackiewicz
Publisher : John Wiley & Sons
ISBN 13 : 0470522151
Total Pages : 500 pages
Book Rating : 4.4/5 (75 download)
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.
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 :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (596 download)
Download or read book Stability of Variable-step Continuous Runge-Kutta Methods for Scalar Delay Differential Equations written by Christopher T. H. Baker and published by . This book was released on 1995 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : S. S. Artemiev
Publisher : Walter de Gruyter
ISBN 13 : 3110944669
Total Pages : 185 pages
Book Rating : 4.1/5 (19 download)
Download or read book Numerical Analysis of Systems of Ordinary and Stochastic Differential Equations written by S. S. Artemiev and published by Walter de Gruyter. This book was released on 2011-02-11 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text deals with numerical analysis of systems of both ordinary and stochastic differential equations. It covers numerical solution problems of the Cauchy problem for stiff ordinary differential equations (ODE) systems by Rosenbrock-type methods (RTMs).
Author : Taketomo Mitsui
Publisher : Springer Nature
ISBN 13 : 9811992630
Total Pages : 118 pages
Book Rating : 4.8/5 (119 download)
Download or read book Numerical Analysis of Ordinary and Delay Differential Equations written by Taketomo Mitsui and published by Springer Nature. This book was released on 2023-05-23 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book serves as a concise textbook for students in an advanced undergraduate or first-year graduate course in various disciplines such as applied mathematics, control, and engineering, who want to understand the modern standard of numerical methods of ordinary and delay differential equations. Experts in the same fields can also learn about the recent developments in numerical analysis of such differential systems. Ordinary differential equations (ODEs) provide a strong mathematical tool to express a wide variety of phenomena in science and engineering. Along with its own significance, one of the powerful directions toward which ODEs extend is to incorporate an unknown function with delayed argument. This is called delay differential equations (DDEs), which often appear in mathematical modelling of biology, demography, epidemiology, and control theory. In some cases, the solution of a differential equation can be obtained by algebraic combinations of known mathematical functions. In many practical cases, however, such a solution is quite difficult or unavailable, and numerical approximations are called for. Modern development of computers accelerates the situation and, moreover, launches more possibilities of numerical means. Henceforth, the knowledge and expertise of the numerical solution of differential equations becomes a requirement in broad areas of science and engineering. One might think that a well-organized software package such as MATLAB serves much the same solution. In a sense, this is true; but it must be kept in mind that blind employment of software packages misleads the user. The gist of numerical solution of differential equations still must be learned. The present book is intended to provide the essence of numerical solutions of ordinary differential equations as well as of delay differential equations. Particularly, the authors noted that there are still few concise textbooks of delay differential equations, and then they set about filling the gap through descriptions as transparent as possible. Major algorithms of numerical solution are clearly described in this book. The stability of solutions of ODEs and DDEs is crucial as well. The book introduces the asymptotic stability of analytical and numerical solutions and provides a practical way to analyze their stability by employing a theory of complex functions.
Author : Robert Mattheij
Publisher : SIAM
ISBN 13 : 0898715318
Total Pages : 408 pages
Book Rating : 4.8/5 (987 download)
Download or read book Ordinary Differential Equations in Theory and Practice written by Robert Mattheij and published by SIAM. This book was released on 1996-01-01 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: In order to emphasize the relationships and cohesion between analytical and numerical techniques, Ordinary Differential Equations in Theory and Practice presents a comprehensive and integrated treatment of both aspects in combination with the modeling of relevant problem classes. This text is uniquely geared to provide enough insight into qualitative aspects of ordinary differential equations (ODEs) to offer a thorough account of quantitative methods for approximating solutions numerically, and to acquaint the reader with mathematical modeling, where such ODEs often play a significant role. Although originally published in 1995, the text remains timely and useful to a wide audience. It provides a thorough introduction to ODEs, since it treats not only standard aspects such as existence, uniqueness, stability, one-step methods, multistep methods, and singular perturbations, but also chaotic systems, differential-algebraic systems, and boundary value problems.
Author : Simeon Ola Fatunla
Publisher :
ISBN 13 :
Total Pages : 320 pages
Book Rating : 4.3/5 (91 download)
Download or read book Numerical Methods for Initial Value Problems in Ordinary Differential Equations written by Simeon Ola Fatunla and published by . This book was released on 1988 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Sylvia Lynn Henderso
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (116 download)
Download or read book The Absolute Stability of Some Discrete Variable Methods in Ordinary Differential Equations written by Sylvia Lynn Henderso and published by . This book was released on 1973 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : J. C. Butcher
Publisher : John Wiley & Sons
ISBN 13 : 1119121507
Total Pages : 546 pages
Book Rating : 4.1/5 (191 download)
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 2016-08-29 with total page 546 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.
Author : Bruce David Link
Publisher :
ISBN 13 :
Total Pages : 234 pages
Book Rating : 4.:/5 (31 download)
Download or read book Numerical Solution of Stiff Ordinary Differential Equations Using Collocation Methods written by Bruce David Link and published by . This book was released on 1976 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Harvard Lomax
Publisher :
ISBN 13 :
Total Pages : 124 pages
Book Rating : 4.:/5 (31 download)
Download or read book An Operational Unification of Finite Difference Methods for the Numerical Integration of Ordinary Differential Equations written by Harvard Lomax and published by . This book was released on 1967 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: One purpose of this report is to present a mathematical procedure which can be used to study and compare various numerical methods for integrating ordinary differential equations. This procedure is relatively simple, mathematically rigorous, and of such a nature that matters of interest in digital computations, such as machine memory and running time, can be weighed against the accuracy and stability provided by the method under consideration. Briefly, the procedure is as follows: (1) Find a single differential equation that is sufficiently representative (this is fully defined in the report) of an arbitrary number of nonhomogeneous, linear, ordinary differential equations with constant coefficients. (2) Solve this differential equation exactly. (3) Choose any given numerical method, use it -- in its entirety -- to reduce the differential equation to difference equations, and, by means of operational techniques, solve the latter exactly. (4) Study and compare the results of (2) and (3). Conceptually there is nothing new in this procedure, but the particular development presented in this report does not appear to have been carried out before. Another purpose is to use the procedure just described to analyze a variety of numerical methods, ranging from classical, predictor-corrector systems to Runge-Kutta techniques and including various combinations of the two.
Author : Lawrence F. Shampine
Publisher : W.H. Freeman
ISBN 13 :
Total Pages : 344 pages
Book Rating : 4.:/5 (5 download)
Download or read book Computer Solution of Ordinary Differential Equations written by Lawrence F. Shampine and published by W.H. Freeman. This book was released on 1975 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : J.R. Dormand
Publisher : CRC Press
ISBN 13 : 1351092006
Total Pages : 349 pages
Book Rating : 4.3/5 (51 download)
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.
Author : John Jacob Kohfeld
Publisher :
ISBN 13 :
Total Pages : 104 pages
Book Rating : 4.:/5 (183 download)
Download or read book Stability of Numerical Solution of Systems of Ordinary Differential Equations written by John Jacob Kohfeld and published by . This book was released on 1963 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: The background for this paper is the use of quadrature formulas for the solution of ordinary differential equations. If we know the values of the dependent variable for which we are solving, and its derivative, at several equally spaced points, i.e., at values of the independent variable separated by equal intervals, we may use a quadrature formula to integrate the values of the derivative, so that we may obtain an approximate value of the dependent variable at the next point. The differential equation is then used to evaluate the derivative at the new point. This procedure is then repeated to evaluate the dependent variable and its derivative at point after point. The accuracy of this method is limited by the accuracy of the quadrature formula used. In order to improve the accuracy of the solution one may use an open-type quadrature formula to "predict" the value of the dependent variable at the next point, then calculate the derivative, and now use a more accurate closed-type formula to "correct" the value of the dependent variable. This procedure is the basis of "Milne's method". It has been shown that an error introduced at a step propagates itself approximately according to a linear combination of the solutions of a linear difference equation associated with the corrector . The solutions of this difference equation consist of an approximation to the solution of the differential equation and in some cases one or more extraneous solutions. If one or more of the latter increases as the process is repeated from step to step, the method is called instable. Remedies for instability include periodic use of special quadrature formulas called "stabilizers". This has been treated in the case of fifth-order formulas by Milne and Reynolds. In this paper the idea is extended to formulas of seventh order.
Author : Randall J. LeVeque
Publisher : SIAM
ISBN 13 : 9780898717839
Total Pages : 356 pages
Book Rating : 4.7/5 (178 download)
Download or read book Finite Difference Methods for Ordinary and Partial Differential Equations written by Randall J. LeVeque and published by SIAM. This book was released on 2007-01-01 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces finite difference methods for both ordinary differential equations (ODEs) and partial differential equations (PDEs) and discusses the similarities and differences between algorithm design and stability analysis for different types of equations. A unified view of stability theory for ODEs and PDEs is presented, and the interplay between ODE and PDE analysis is stressed. The text emphasizes standard classical methods, but several newer approaches also are introduced and are described in the context of simple motivating examples.
Author : Ernst Hairer
Publisher : Springer Science & Business Media
ISBN 13 :
Total Pages : 504 pages
Book Rating : 4.:/5 (318 download)
Download or read book Solving Ordinary Differential Equations written by Ernst Hairer and published by Springer Science & Business Media. This book was released on 1987 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt:
