Parameter Uniform Numerical Methods For Singular Perturbation Problems
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Fitted Numerical Methods For Singular Perturbation Problems
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Author : John J. H. Miller
language : en
Publisher: World Scientific
Release Date : 2012
Fitted Numerical Methods For Singular Perturbation Problems written by John J. H. Miller and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.
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.
Parameter Uniform Numerical Methods For Singular Perturbation Problems
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Author : Jugal Mohapatra
language : en
Publisher: LAP Lambert Academic Publishing
Release Date : 2012-04
Parameter Uniform Numerical Methods For Singular Perturbation Problems written by Jugal Mohapatra and has been published by LAP Lambert Academic Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04 with categories.
Singularly perturbed boundary-value problems(SPP) arise in several branches of engineering and applied mathematics where the edge effects are important. These problems are often described by differential equations where the highest order derivative is multiplied by an arbitrarily small parameter` `known as the singular perturbation parameter. The solution of these problems possesses boundary (or interior) layers which are thin narrow regions in the neighborhood of the boundary (or interior) of the domain, where the gradient of the solution becomes very high as goes to zero. Classical numerical schemes fails to yield satisfactory numerical approximations on uniform grids due to the presence of boundary layers. To solve SPP, fitted mesh methods are often followed which comprise of standard finite difference operators on specially designed meshes. The aim of this book revolves around developing, analyzing and optimizing the -uniform upwind based fitted mesh methods resolving the convection-dominated layer type problems using non uniform grids.
Fitted Numerical Methods For Singular Perturbation Problems Error Estimates In The Maximum Norm For Linear Problems In One And Two Dimensions
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Author : John J H Miller
language : en
Publisher: World Scientific
Release Date : 1996-01-01
Fitted Numerical Methods For Singular Perturbation Problems Error Estimates In The Maximum Norm For Linear Problems In One And Two Dimensions written by John J H Miller and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-01-01 with Mathematics categories.
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 this 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.
Robust Numerical Methods For Singularly Perturbed Differential Equations
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Author : Hans-G. Roos
language : en
Publisher: Springer
Release Date : 2010-11-18
Robust Numerical Methods For Singularly Perturbed Differential Equations written by Hans-G. Roos and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-11-18 with Mathematics categories.
This new edition incorporates new developments in numerical methods for singularly perturbed differential equations, focusing on linear convection-diffusion equations and on nonlinear flow problems that appear in computational fluid dynamics.
Numerical Continuation Methods
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Author : Eugene L. Allgower
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Numerical Continuation Methods written by Eugene L. Allgower and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Over the past fifteen years two new techniques have yielded extremely important contributions toward the numerical solution of nonlinear systems of equations. This book provides an introduction to and an up-to-date survey of numerical continuation methods (tracing of implicitly defined curves) of both predictor-corrector and piecewise-linear types. It presents and analyzes implementations aimed at applications to the computation of zero points, fixed points, nonlinear eigenvalue problems, bifurcation and turning points, and economic equilibria. Many algorithms are presented in a pseudo code format. An appendix supplies five sample FORTRAN programs with numerical examples, which readers can adapt to fit their purposes, and a description of the program package SCOUT for analyzing nonlinear problems via piecewise-linear methods. An extensive up-to-date bibliography spanning 46 pages is included. The material in this book has been presented to students of mathematics, engineering and sciences with great success, and will also serve as a valuable tool for researchers in the field.
Robust Computational Techniques For Boundary Layers
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Author : Paul Farrell
language : en
Publisher: CRC Press
Release Date : 2000-03-30
Robust Computational Techniques For Boundary Layers written by Paul Farrell and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-03-30 with Science categories.
Current standard numerical methods are of little use in solving mathematical problems involving boundary layers. In Robust Computational Techniques for Boundary Layers, the authors construct numerical methods for solving problems involving differential equations that have non-smooth solutions with singularities related to boundary layers. They present a new numerical technique that provides precise results in the boundary layer regions for the problems discussed in the book. They show that this technique can be adapted in a natural way to a real flow problem, and that it can be used to construct benchmark solutions for comparison with solutions found using other numerical techniques. Focusing on robustness, simplicity, and wide applicability rather than on optimality, Robust Computational Techniques for Boundary Layers provides readers with an understanding of the underlying principles and the essential components needed for the construction of numerical methods for boundary layer problems. It explains the fundamental ideas through physical insight, model problems, and computational experiments and gives details of the linear solvers used in the computations so that readers can implement the methods and reproduce the numerical results.
Difference Methods For Singular Perturbation Problems
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Author : Grigory I. Shishkin
language : en
Publisher: CRC Press
Release Date : 2008-09-22
Difference Methods For Singular Perturbation Problems written by Grigory I. Shishkin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-09-22 with Mathematics categories.
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
Numerical Solution Of Boundary Value Problems For Ordinary Differential Equations
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Author : Uri M. Ascher
language : en
Publisher: SIAM
Release Date : 1988-01-01
Numerical Solution Of Boundary Value Problems For Ordinary Differential Equations written by Uri M. Ascher and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-01-01 with Mathematics categories.
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.
Robust Numerical Methods For Singularly Perturbed Differential Equations
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Author : Hans-Görg Roos
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-09-17
Robust Numerical Methods For Singularly Perturbed Differential Equations written by Hans-Görg Roos and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-09-17 with Mathematics categories.
This new edition incorporates new developments in numerical methods for singularly perturbed differential equations, focusing on linear convection-diffusion equations and on nonlinear flow problems that appear in computational fluid dynamics.
Differential Equations And Numerical Analysis
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Author : Valarmathi Sigamani
language : en
Publisher: Springer
Release Date : 2016-08-17
Differential Equations And Numerical Analysis written by Valarmathi Sigamani and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-17 with Mathematics categories.
This book offers an ideal introduction to singular perturbation problems, and a valuable guide for researchers in the field of differential equations. It also includes chapters on new contributions to both fields: differential equations and singular perturbation problems. Written by experts who are active researchers in the related fields, the book serves as a comprehensive source of information on the underlying ideas in the construction of numerical methods to address different classes of problems with solutions of different behaviors, which will ultimately help researchers to design and assess numerical methods for solving new problems. All the chapters presented in the volume are complemented by illustrations in the form of tables and graphs.