Analytical And Numerical Methods For Convection Dominated And Singularly Perturbed Problems
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| Author | : Lubin Vulkov |
| Publisher | : Nova Publishers |
| Total Pages | : 298 |
| Release | : 2000 |
| Genre | : Mathematics |
| ISBN | : 9781560728481 |
This volume is the Proceedings of the Workshop on Analytical and Computational Methods for Convection-Dominated and Singularly Perturbed Problems, which took place in Lozenetz, Bulgaria, 27-31 August 1998. The workshop attracted about 50 participants from 12 countries. The volume includes 13 invited lectures and 19 contributed papers presented at the workshop and thus gives an overview of the latest developments in both the theory and applications of advanced numerical methods to problems having boundary and interior layers. There was an emphasis on experiences from the numerical analysis of such problems and on theoretical developments. The aim of the workshop was to provide an opportunity for scientists from the East and the West, who develop robust methods for singularly perturbed and related problems and also who apply these methods to real-life problems, to discuss recent achievements in this area and to exchange ideas with a view of possible research co-operation.
| 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.
| 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.
| Author | : Hans-Görg Roos |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 364 |
| Release | : 2013-06-29 |
| Genre | : Mathematics |
| ISBN | : 3662032066 |
The analysis of singular perturbed differential equations began early in this century, when approximate solutions were constructed from asymptotic ex pansions. (Preliminary attempts appear in the nineteenth century [vD94].) This technique has flourished since the mid-1960s. Its principal ideas and methods are described in several textbooks. Nevertheless, asymptotic ex pansions may be impossible to construct or may fail to simplify the given problem; then numerical approximations are often the only option. The systematic study of numerical methods for singular perturbation problems started somewhat later - in the 1970s. While the research frontier has been steadily pushed back, the exposition of new developments in the analysis of numerical methods has been neglected. Perhaps the only example of a textbook that concentrates on this analysis is [DMS80], which collects various results for ordinary differential equations, but many methods and techniques that are relevant today (especially for partial differential equa tions) were developed after 1980.Thus contemporary researchers must comb the literature to acquaint themselves with earlier work. Our purposes in writing this introductory book are twofold. First, we aim to present a structured account of recent ideas in the numerical analysis of singularly perturbed differential equations. Second, this important area has many open problems and we hope that our book will stimulate further investigations.Our choice of topics is inevitably personal and reflects our own main interests.
| Author | : Lubin Vulkov |
| Publisher | : Springer |
| Total Pages | : 803 |
| Release | : 2003-07-31 |
| Genre | : Mathematics |
| ISBN | : 3540452621 |
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.
| Author | : Jagdev Singh |
| Publisher | : Springer Nature |
| Total Pages | : 589 |
| Release | : 2023-04-12 |
| Genre | : Technology & Engineering |
| ISBN | : 3031299590 |
The book is very useful for researchers, graduate students and educators associated with or interested in recent advances in different aspects of modelling, computational methods and techniques necessary for solving problems arising in the real-world problems. The book includes carefully peer-reviewed research articles presented in the “5th International Conference on Mathematical Modelling, Applied Analysis and Computation”, held at JECRC University, Jaipur, during 4–6 August 2022 concentrating on current advances in mathematical modelling and computation via tools and techniques from mathematics and allied areas. It is focused on papers dealing with necessary theory and methods in a balanced manner and contributes towards solving problems arising in engineering, control systems, networking system, environment science, health science, physical and biological systems, social issues of current interest, etc.
| Author | : Martin Stynes |
| Publisher | : |
| Total Pages | : |
| Release | : 2018 |
| Genre | : MATHEMATICS |
| ISBN | : 9781470450212 |
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 c.
| Author | : Ivan Dimov |
| Publisher | : Springer |
| Total Pages | : 583 |
| Release | : 2013-10-01 |
| Genre | : Computers |
| ISBN | : 3642415156 |
This book constitutes thoroughly revised selected papers of the 5th International Conference on Numerical Analysis and Its Applications, NAA 2012, held in Lozenetz, Bulgaria, in June 2012. The 65 revised papers presented were carefully reviewed and selected from various submissions. The papers cover a broad area of topics of interest such as numerical approximation and computational geometry; numerical linear algebra and numerical solution of transcendental equation; numerical methods for differential equations; numerical stochastics, numerical modeling; and high performance scientific computing.
| Author | : Torsten Linß |
| Publisher | : Springer |
| Total Pages | : 331 |
| Release | : 2009-11-21 |
| Genre | : Mathematics |
| ISBN | : 3642051340 |
This is a book on numerical methods for singular perturbation problems – in part- ular, stationary reaction-convection-diffusion problems exhibiting layer behaviour. More precisely, it is devoted to the construction and analysis of layer-adapted meshes underlying these numerical methods. Numerical methods for singularly perturbed differential equations have been studied since the early 1970s and the research frontier has been constantly - panding since. A comprehensive exposition of the state of the art in the analysis of numerical methods for singular perturbation problems is [141] which was p- lished in 2008. As that monograph covers a big variety of numerical methods, it only contains a rather short introduction to layer-adapted meshes, while the present book is exclusively dedicated to that subject. An early important contribution towards the optimisation of numerical methods by means of special meshes was made by N.S. Bakhvalov [18] in 1969. His paper spawned a lively discussion in the literature with a number of further meshes - ing proposed and applied to various singular perturbation problems. However, in the mid 1980s, this development stalled, but was enlivened again by G.I. Shishkin’s proposal of piecewise-equidistant meshes in the early 1990s [121,150]. Because of their very simple structure, they are often much easier to analyse than other meshes, although they give numerical approximations that are inferior to solutions on c- peting meshes. Shishkin meshes for numerous problems and numerical methods have been studied since and they are still very much in vogue.
| Author | : Paul Farrell |
| Publisher | : CRC Press |
| Total Pages | : 298 |
| Release | : 2000-03-30 |
| Genre | : Science |
| ISBN | : 9781584881926 |
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.
