Fitted Numerical Methods For Singular Perturbation Problems

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Fitted Numerical Methods For Singular Perturbation Problems Error Estimates In The Maximum Norm For Linear Problems In One And Two Dimensions Revised Edition

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Author : John J H Miller
language : en
Publisher: World Scientific
Release Date : 2012-02-29

Fitted Numerical Methods For Singular Perturbation Problems Error Estimates In The Maximum Norm For Linear Problems In One And Two Dimensions Revised Edition 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 2012-02-29 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.

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.

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

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.

Numerical Analysis And Its Applications

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Author : Svetozar Margenov
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-03-09

Numerical Analysis And Its Applications written by Svetozar Margenov 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 2009-03-09 with Computers categories.

This book constitutes the thoroughly refereed post-conference proceedings of the 4th International Conference on Numerical Analysis and Its Applications, NAA 2008, held in Lozenetz, Bulgaria in June 2008. The 61 revised full papers presented together with 13 invited papers were carefully selected during two rounds of reviewing and improvement. The papers address all current aspects of numerical analysis and discuss a wide range of problems concerning recent achievements in physics, chemistry, engineering, and economics. A special focus is given to numerical approximation and computational geometry, numerical linear algebra and numerical solution of transcendental equations, numerical methods for differential equations, numerical modeling, and high performance scientific computing.

Hp Finite Element Methods For Singular Perturbations

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Author : Jens M. Melenk
language : en
Publisher: Springer
Release Date : 2004-10-19

Hp Finite Element Methods For Singular Perturbations written by Jens M. Melenk and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-10-19 with Mathematics categories.

Many partial differential equations arising in practice are parameter-dependent problems that are of singularly perturbed type. Prominent examples include plate and shell models for small thickness in solid mechanics, convection-diffusion problems in fluid mechanics, and equations arising in semi-conductor device modelling. Common features of these problems are layers and, in the case of non-smooth geometries, corner singularities. Mesh design principles for the efficient approximation of both features by the hp-version of the finite element method (hp-FEM) are proposed in this volume. For a class of singularly perturbed problems on polygonal domains, robust exponential convergence of the hp-FEM based on these mesh design principles is established rigorously.

Applications Of Nonstandard Finite Difference Schemes

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Author : Ronald E. Mickens
language : en
Publisher: World Scientific
Release Date : 2000

Applications Of Nonstandard Finite Difference Schemes written by Ronald E. Mickens and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.

The main purpose of this book is to provide a concise introduction to the methods and philosophy of constructing nonstandard finite difference schemes and illustrate how such techniques can be applied to several important problems. Chapter I gives an overview of the subject and summarizes previous work. Chapters 2 and 3 consider in detail the construction and numerical implementation of schemes for physical problems involving convection-diffusion-reaction equations, that arise in groundwater pollution and scattering of electromagnetic waves using Maxwell's equations. Chapter 4 examines certain mathematical issues related to the nonstandard discretization of competitive and cooperative models for ecology. The application chapters illustrate well the power of nonstandard methods. In particular, for the same accuracy as obtained by standard techniques, larger step sizes can be used. This volume will satisfy the needs of scientists, engineers, and mathematicians who wish to know how to construct nonstandard schemes and see how these are applied to obtain numerical solutions of the differential equations which arise in the study of nonlinear dynamical systems modeling important physical phenomena.

Solving Least Squares Problems

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Author : Charles L. Lawson
language : en
Publisher: SIAM
Release Date : 1995-12-01

Solving Least Squares Problems written by Charles L. Lawson and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-12-01 with Mathematics categories.

This Classic edition includes a new appendix which summarizes the major developments since the book was originally published in 1974. The additions are organized in short sections associated with each chapter. An additional 230 references have been added, bringing the bibliography to over 400 entries. Appendix C has been edited to reflect changes in the associated software package and software distribution method.

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.

Layer Resolving Grids And Transformations For Singular Perturbation Problems

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Author : Vladimir D. Liseikin
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2018-11-05

Layer Resolving Grids And Transformations For Singular Perturbation Problems written by Vladimir D. Liseikin and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-05 with Mathematics categories.

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