Numerical Methods For Stiff Equations And Singular Perturbation Problems

Author : A. Miranker
Publisher : Springer
Page : 0 pages
File Size : 44,9 Mb
Release : 2001-12-14
Category : Computers
ISBN : 9400987722

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Numerical Methods for Stiff Equations and Singular Perturbation Problems by A. Miranker Pdf

Approach your problems from It isn't that they can't see the the right end and begin with the solution. It is that they can't see the problem. answers. Then, one day, perhaps you will find the final question. The Hermit Clad in Crane Feathers' G. K. Chesterton, The scandal of in R. Van Gulik's The Chinese Maze Father Brown "The point ofa pin" Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the 'tree' of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces.

Author : John James Henry Miller,Eugene O'Riordan,G. I. Shishkin
Publisher : World Scientific
Page : 191 pages
File Size : 49,9 Mb
Release : 2012
Category : Mathematics
ISBN : 9789814390736

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Fitted Numerical Methods for Singular Perturbation Problems by John James Henry Miller,Eugene O'Riordan,G. I. Shishkin Pdf

Since the first edition of this book, the literature on fitted mesh methods for singularly perturbed problems has expanded significantly. Over the intervening years, fitted meshes have been shown to be effective for an extensive set of singularly perturbed partial differential equations. In the revised version of this book, the reader will find an introduction to the basic theory associated with fitted numerical methods for singularly perturbed differential equations. Fitted mesh methods focus on the appropriate distribution of the mesh points for singularly perturbed problems. The global errors in the numerical approximations are measured in the pointwise maximum norm. The fitted mesh algorithm is particularly simple to implement in practice, but the theory of why these numerical methods work is far from simple. This book can be used as an introductory text to the theory underpinning fitted mesh methods.

Author : A. Miranker
Publisher : Springer Science & Business Media
Page : 224 pages
File Size : 40,8 Mb
Release : 2001-11-30
Category : Computers
ISBN : 140200298X

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Numerical Methods for Stiff Equations and Singular Perturbation Problems by A. Miranker Pdf

Approach your problems from It isn't that they can't see the the right end and begin with the solution. It is that they can't see the problem. answers. Then, one day, perhaps you will find the final question. The Hermit Clad in Crane Feathers' G. K. Chesterton, The scandal of in R. Van Gulik's The Chinese Maze Father Brown "The point ofa pin" Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the 'tree' of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces.

Author : P. W. Hemker,John James Henry Miller
Publisher : Unknown
Page : 520 pages
File Size : 52,7 Mb
Release : 1979
Category : Mathematics
ISBN : UOM:39015009241061

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Numerical Analysis of Singular Perturbation Problems by P. W. Hemker,John James Henry Miller Pdf

14 lectures by the invited speakers and 14 shorter contributions from the other speakers (pref.)

Author : Ernst Hairer,Gerhard Wanner
Publisher : Springer Science & Business Media
Page : 615 pages
File Size : 45,8 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9783662099476

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Solving Ordinary Differential Equations II by Ernst Hairer,Gerhard Wanner Pdf

"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.

Author : Ernst Hairer,Syvert Paul Nørsett,Gerhard Wanner
Publisher : Springer
Page : 632 pages
File Size : 54,9 Mb
Release : 1987
Category : Mathematics
ISBN : UOM:39015025215727

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Solving Ordinary Differential Equations II by Ernst Hairer,Syvert Paul Nørsett,Gerhard Wanner Pdf

"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.

Author : Uri M. Ascher,Robert M. M. Mattheij,Robert D. Russell
Publisher : SIAM
Page : 617 pages
File Size : 52,6 Mb
Release : 1988-01-01
Category : Mathematics
ISBN : 9780898713541

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Numerical Solution of Boundary Value Problems for Ordinary Differential Equations by Uri M. Ascher,Robert M. M. Mattheij,Robert D. Russell Pdf

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 : Ralph Willoughby
Publisher : Springer Science & Business Media
Page : 324 pages
File Size : 54,6 Mb
Release : 2013-03-13
Category : Science
ISBN : 9781468421002

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Stiff Differential Systems by Ralph Willoughby Pdf

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 : Ülo Lepik,Helle Hein
Publisher : Springer Science & Business Media
Page : 209 pages
File Size : 53,5 Mb
Release : 2014-01-09
Category : Technology & Engineering
ISBN : 9783319042954

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Haar Wavelets by Ülo Lepik,Helle Hein Pdf

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 : Willard L. Miranker
Publisher : Unknown
Page : 240 pages
File Size : 40,8 Mb
Release : 1976
Category : Differential equations
ISBN : UOM:39015049308557

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The Computational Theory of Stiff Differential Equations by Willard L. Miranker Pdf

Author : Hans-Görg Roos
Publisher : Unknown
Page : 348 pages
File Size : 44,6 Mb
Release : 1996
Category : Differential equations
ISBN : 3662032082

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Numerical Methods for Singularly Perturbed Differential Equations by Hans-Görg Roos Pdf

This book collects, explains and analyses basic methods and recent results for the successful numerical solution of singularly perturbed differential equations. Such equations model many physical phenomena and their solutions are characterized by the presence of layers. The book is a wide-ranging introduction to the exciting current literature in this area. It concentrates on linear convection-diffusion equations and related nonlinear flow problems, encompassing both ordinary and partial differential equations. While many numerical methods are considered, particular attention is paid to those with realistic error estimates. The book provides a solid and thorough foundation for the numerical analysis and solution of singular perturbation problems.

Author : Richard C. Aiken
Publisher : Oxford University Press, USA
Page : 490 pages
File Size : 50,5 Mb
Release : 1985
Category : History
ISBN : UOM:39015048138849

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Stiff Computation by Richard C. Aiken Pdf

Author : Grigory I. Shishkin,Lidia P. Shishkina
Publisher : CRC Press
Page : 409 pages
File Size : 50,5 Mb
Release : 2008-09-22
Category : Mathematics
ISBN : 9780203492413

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Difference Methods for Singular Perturbation Problems by Grigory I. Shishkin,Lidia P. Shishkina Pdf

Difference Methods for Singular Perturbation Problems focuses on the development of robust difference schemes for wide classes of boundary value problems. It justifies the ε-uniform convergence of these schemes and surveys the latest approaches important for further progress in numerical methods. The first part of the book e

Author : Robert E., Jr. O'Malley
Publisher : Springer Science & Business Media
Page : 234 pages
File Size : 41,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461209775

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Singular Perturbation Methods for Ordinary Differential Equations by Robert E., Jr. O'Malley Pdf

This book results from various lectures given in recent years. Early drafts were used for several single semester courses on singular perturbation meth ods given at Rensselaer, and a more complete version was used for a one year course at the Technische Universitat Wien. Some portions have been used for short lecture series at Universidad Central de Venezuela, West Vir ginia University, the University of Southern California, the University of California at Davis, East China Normal University, the University of Texas at Arlington, Universita di Padova, and the University of New Hampshire, among other places. As a result, I've obtained lots of valuable feedback from students and listeners, for which I am grateful. This writing continues a pattern. Earlier lectures at Bell Laboratories, at the University of Edin burgh and New York University, and at the Australian National University led to my earlier works (1968, 1974, and 1978). All seem to have been useful for the study of singular perturbations, and I hope the same will be true of this monograph. I've personally learned much from reading and analyzing the works of others, so I would especially encourage readers to treat this book as an introduction to a diverse and exciting literature. The topic coverage selected is personal and reflects my current opin ions. An attempt has been made to encourage a consistent method of ap proaching problems, largely through correcting outer limits in regions of rapid change. Formal proofs of correctness are not emphasized.

Author : G. Hall,James Murray Watt
Publisher : Oxford University Press, USA
Page : 358 pages
File Size : 44,8 Mb
Release : 1976
Category : Boundary value problems
ISBN : UCAL:B4406402

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Modern Numerical Methods for Ordinary Differential Equations by G. Hall,James Murray Watt Pdf