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

Fitted Numerical Methods For Singular Perturbation Problems: Error Estimates In The Maximum Norm For Linear Problems In One And Two Dimensions (Revised Edition)
Author: John J H Miller
Publisher: World Scientific
Total Pages: 191
Release: 2012-02-29
Genre: Mathematics
ISBN: 9814452777

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

Fitted Numerical Methods for Singular Perturbation Problems
Author: John J. H. Miller
Publisher: World Scientific
Total Pages: 191
Release: 2012
Genre: Mathematics
ISBN: 9814390747

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

Fitted Numerical Methods for Singular Perturbation Problems
Author: John James Henry Miller
Publisher: World Scientific
Total Pages: 191
Release: 2012
Genre: Mathematics
ISBN: 9814390739

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.

Robust Numerical Methods for Singularly Perturbed Differential Equations

Robust Numerical Methods for Singularly Perturbed Differential Equations
Author: Hans-Görg Roos
Publisher: Springer Science & Business Media
Total Pages: 599
Release: 2008-09-17
Genre: Mathematics
ISBN: 3540344675

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 Applications

Differential Equations and Applications
Author: Valarmathi Sigamani
Publisher: Springer Nature
Total Pages: 218
Release: 2022-01-24
Genre: Mathematics
ISBN: 9811675465

This book collects select papers presented at the International Conference on Applications of Basic Sciences, held at Tiruchirappalli, Tamil Nadu, India, from 19-21 November 2019. The book discusses topics on singular perturbation problems, differential equations, numerical analysis, fuzzy logics, fuzzy differential equations, and mathematical physics, and their interdisciplinary applications in all areas of basic sciences: mathematics, physics, chemistry, and biology. It will be useful to researchers and scientists in all disciplines of basic sciences. This book will be very useful to know the different scientific approaches for a single physical system.

Introduction to Singular Perturbations

Introduction to Singular Perturbations
Author: Robert E. Jr. O'Malley
Publisher: Elsevier
Total Pages: 215
Release: 2012-12-02
Genre: Mathematics
ISBN: 0323162274

Introduction to Singular Perturbations provides an overview of the fundamental techniques for obtaining asymptomatic solutions to boundary value problems. This text explores singular perturbation techniques, which are among the basic tools of several applied scientists. This book is organized into eight chapters, wherein Chapter 1 discusses the method of matched asymptomatic expansions, which has been frequently applied to several physical problems involving singular perturbations. Chapter 2 considers the nonlinear initial value problem to illustrate the regular perturbation method, and Chapter 3 explains how to construct asymptotic solutions for general linear equations. Chapter 4 discusses scalar equations and nonlinear system, whereas Chapters 5 and 6 explain the contrasts for initial value problems where the outer expansion cannot be determined without obtaining the initial values of the boundary layer correction. Chapters 7 and 8 deal with boundary value problem that arises in the study of adiabatic tubular chemical flow reactors with axial diffusion. This monograph is a valuable resource for applied mathematicians, engineers, researchers, students, and readers whose interests span a variety of fields.

Difference Methods for Singular Perturbation Problems

Difference Methods for Singular Perturbation Problems
Author: Grigory I. Shishkin
Publisher: CRC Press
Total Pages: 409
Release: 2008-09-22
Genre: Mathematics
ISBN: 0203492412

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 Analysis and Its Applications

Numerical Analysis and Its Applications
Author: Svetozar Margenov
Publisher: Springer Science & Business Media
Total Pages: 646
Release: 2009-03-09
Genre: Computers
ISBN: 3642004636

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.

Numerical Methods for Chemical Engineering

Numerical Methods for Chemical Engineering
Author: Kenneth J. Beers
Publisher: Cambridge University Press
Total Pages: 496
Release: 2007
Genre: Computers
ISBN: 9780521859714

Applications of numerical mathematics and scientific computing to chemical engineering.

Frontiers In Mathematical Analysis And Numerical Methods: In Memory Of Jacques-louis Lions

Frontiers In Mathematical Analysis And Numerical Methods: In Memory Of Jacques-louis Lions
Author: Tatsien Li
Publisher: World Scientific
Total Pages: 306
Release: 2004-07-26
Genre: Mathematics
ISBN: 9814482145

This invaluable volume is a collection of articles in memory of Jacques-Louis Lions, a leading mathematician and the founder of the Contemporary French Applied Mathematics School. The contributions have been written by his friends, colleagues and students, including C Bardos, A Bensoussan, S S Chern, P G Ciarlet, R Glowinski, Gu Chaohao, B Malgrange, G Marchuk, O Pironneau, W Strauss, R Temam, etc.The book concerns many important results in analysis, geometry, numerical methods, fluid mechanics, control theory, etc.