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

Published: 2012-02-29

Total Pages: 191

ISBN-13: 9814452777

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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.


Convection-Diffusion Problems

Convection-Diffusion Problems

Author: Martin Stynes

Publisher: American Mathematical Soc.

Published: 2018-11-21

Total Pages: 168

ISBN-13: 1470448688

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Many physical problems involve diffusive and convective (transport) processes. When diffusion dominates convection, standard numerical methods work satisfactorily. But when convection dominates diffusion, the standard methods become unstable, and special techniques are needed to compute accurate numerical approximations of the unknown solution. This convection-dominated regime is the focus of the book. After discussing at length the nature of solutions to convection-dominated convection-diffusion problems, the authors motivate and design numerical methods that are particularly suited to this class of problems. At first they examine finite-difference methods for two-point boundary value problems, as their analysis requires little theoretical background. Upwinding, artificial diffusion, uniformly convergent methods, and Shishkin meshes are some of the topics presented. Throughout, the authors are concerned with the accuracy of solutions when the diffusion coefficient is close to zero. Later in the book they concentrate on finite element methods for problems posed in one and two dimensions. This lucid yet thorough account of convection-dominated convection-diffusion problems and how to solve them numerically is meant for beginning graduate students, and it includes a large number of exercises. An up-to-date bibliography provides the reader with further reading.


Finite Difference Methods,Theory and Applications

Finite Difference Methods,Theory and Applications

Author: Ivan Dimov

Publisher: Springer

Published: 2015-06-16

Total Pages: 443

ISBN-13: 3319202391

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This book constitutes the thoroughly refereed post-conference proceedings of the 6th International Conference on Finite Difference Methods, FDM 2014, held in Lozenetz, Bulgaria, in June 2014. The 36 revised full papers were carefully reviewed and selected from 62 submissions. These papers together with 12 invited papers cover topics such as finite difference and combined finite difference methods as well as finite element methods and their various applications in physics, chemistry, biology and finance.


Historical Developments in Singular Perturbations

Historical Developments in Singular Perturbations

Author: Robert E. O'Malley

Publisher: Springer

Published: 2014-11-19

Total Pages: 263

ISBN-13: 3319119249

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This engaging text describes the development of singular perturbations, including its history, accumulating literature, and its current status. While the approach of the text is sophisticated, the literature is accessible to a broad audience. A particularly valuable bonus are the historical remarks. These remarks are found throughout the manuscript. They demonstrate the growth of mathematical thinking on this topic by engineers and mathematicians. The book focuses on detailing how the various methods are to be applied. These are illustrated by a number and variety of examples. Readers are expected to have a working knowledge of elementary ordinary differential equations, including some familiarity with power series techniques, and of some advanced calculus. Dr. O'Malley has written a number of books on singular perturbations. This book has developed from many of his works in the field of perturbation theory.


Numerical Analysis and Its Applications

Numerical Analysis and Its Applications

Author: Zhilin Li

Publisher: Springer

Published: 2005-02-07

Total Pages: 642

ISBN-13: 3540318526

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This book constitutes the thoroughly refereed post-proceedings of the Third International Conference on Numerical Analysis and Its Applications, NAA 2004, held in Rousse, Bulgaria in June/July 2004. The 68 revised full papers presented together with 8 invited papers were carefully selected during two rounds of reviewing and improvement. All current aspects of numerical analysis are addressed. Among the application fields covered are computational sciences and engineering, chemistry, physics, economics, simulation, fluid dynamics, visualization, etc.


Advances in Applied Mathematics

Advances in Applied Mathematics

Author: Ali R. Ansari

Publisher: Springer

Published: 2014-08-04

Total Pages: 276

ISBN-13: 3319069233

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This volume contains contributions from the Gulf International Conference in Applied Mathematics, held at the Gulf University for Science & Technology. The proceedings reflects the three major themes of the conference. The first of these was mathematical biology, including a keynote address by Professor Philip Maini. The second theme was computational science/numerical analysis, including a keynote address by Professor Grigorii Shishkin. The conference also addressed more general applications topics, with papers in business applications, fluid mechanics, optimization, scheduling problems and engineering applications, as well as a keynote by Professor Ali Nayfeh.


Numerical Analysis and Its Applications

Numerical Analysis and Its Applications

Author: Svetozar Margenov

Publisher: Springer Science & Business Media

Published: 2009-03-09

Total Pages: 646

ISBN-13: 3642004636

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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.


Difference Methods for Singular Perturbation Problems

Difference Methods for Singular Perturbation Problems

Author: Grigory I. Shishkin

Publisher: CRC Press

Published: 2008-09-22

Total Pages: 409

ISBN-13: 0203492412

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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: Lubin Vulkov

Publisher: Springer

Published: 2003-07-31

Total Pages: 803

ISBN-13: 3540452621

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This book constitutes the thoroughly refereed post-proceedings of the Second International Conference on Numerical Analysis and Its Applications, NAA 2000, held in Rousse, Bulgaria in June 2000.The 90 revised papers presented were carefully selected for inclusion in the book during the two rounds of inspection and reviewing. All current aspects of numerical analysis are addressed. Among the application fields covered are computational sciences and engineering, chemistry, physics, economics, simulation, etc.


Fourteenth International Conference Zaragoza–Pau on Mathematics and its Applications

Fourteenth International Conference Zaragoza–Pau on Mathematics and its Applications

Author: López de Silanes, M. C.

Publisher: Prensas de la Universidad de Zaragoza

Published: 2018-02-20

Total Pages: 242

ISBN-13: 8417358005

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The International Conference Zaragoza-Pau on Mathematics and its Applications was organized by the Departamento de Matemática Aplicada, the Departamento de Métodos Estadísticos and the Departamento de Matemáticas, all of them from the Universidad de Zaragoza (Spain), and the Laboratoire de Mathématiques et de leurs Applications, from the Université de Pau et des Pays de l’Adour (France). This conference has been held every two years since 1989. The aim of this conference is to present recent advances in Applied Mathematics, Statistics and Pure Mathematics, putting special emphasis on subjects linked to petroleum engineering and environmental problems. The Fourteenth Conference took place in Jaca (Spain) from 12nd to 15th September 2016. During those four days, 99 mathematicians, coming from di erent universities, research institutes or the industrial sector, attended 14 plenary lectures, 62 contributed talks and a poster session with 4 posters. We note that in this edition there were 11 mini-symposia, two of them co-organized by colleagues from the Universidad de Zaragoza and the Université de Pau et des Pays de l’Adour.