Analytical And Numerical Methods For Convection Dominated And Singularly Perturbed Problems

Author : Lubin Vulkov,John James Henry Miller
Publisher : Nova Publishers
Page : 298 pages
File Size : 41,8 Mb
Release : 2000
Category : Mathematics
ISBN : 1560728485

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Analytical and Numerical Methods for Convection-dominated and Singularly Perturbed Problems by Lubin Vulkov,John James Henry Miller Pdf

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,Martin Stynes,Lutz Tobiska
Publisher : Springer Science & Business Media
Page : 599 pages
File Size : 55,8 Mb
Release : 2008-09-17
Category : Mathematics
ISBN : 9783540344674

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Robust Numerical Methods for Singularly Perturbed Differential Equations by Hans-Görg Roos,Martin Stynes,Lutz Tobiska Pdf

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 : Martin Stynes,David Stynes
Publisher : Unknown
Page : 128 pages
File Size : 42,5 Mb
Release : 2018
Category : MATHEMATICS
ISBN : 1470450216

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Convection-diffusion Problems by Martin Stynes,David Stynes Pdf

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 : Martin Stynes,David Stynes
Publisher : American Mathematical Soc.
Page : 156 pages
File Size : 48,5 Mb
Release : 2018-11-21
Category : Differential equations
ISBN : 9781470448684

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Convection-Diffusion Problems: An Introduction to Their Analysis and Numerical Solution by Martin Stynes,David Stynes Pdf

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.

Author : Jagdev Singh,George A. Anastassiou,Dumitru Baleanu,Devendra Kumar
Publisher : Springer Nature
Page : 589 pages
File Size : 55,6 Mb
Release : 2023-04-12
Category : Technology & Engineering
ISBN : 9783031299599

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Advances in Mathematical Modelling, Applied Analysis and Computation by Jagdev Singh,George A. Anastassiou,Dumitru Baleanu,Devendra Kumar Pdf

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 : Valarmathi Sigamani,John J. H. Miller,Ramanujam Narasimhan,Paramasivam Mathiazhagan,Franklin Victor
Publisher : Springer
Page : 165 pages
File Size : 46,6 Mb
Release : 2016-08-17
Category : Mathematics
ISBN : 9788132235989

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Differential Equations and Numerical Analysis by Valarmathi Sigamani,John J. H. Miller,Ramanujam Narasimhan,Paramasivam Mathiazhagan,Franklin Victor Pdf

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.

Author : Paul Farrell,Alan Hegarty,John M. Miller,Eugene O'Riordan,Grigory I. Shishkin
Publisher : CRC Press
Page : 256 pages
File Size : 40,7 Mb
Release : 2000-03-30
Category : Computers
ISBN : 9781482285727

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Robust Computational Techniques for Boundary Layers by Paul Farrell,Alan Hegarty,John M. Miller,Eugene O'Riordan,Grigory I. Shishkin Pdf

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 pres

Author : Torsten Linß
Publisher : Springer
Page : 331 pages
File Size : 40,7 Mb
Release : 2009-11-21
Category : Mathematics
ISBN : 9783642051340

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Layer-Adapted Meshes for Reaction-Convection-Diffusion Problems by Torsten Linß Pdf

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 : Lubin Vulkov,Jerzy Wasniewski,Plamen Yalamov
Publisher : Springer
Page : 790 pages
File Size : 51,9 Mb
Release : 2003-07-31
Category : Mathematics
ISBN : 9783540452621

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Numerical Analysis and Its Applications by Lubin Vulkov,Jerzy Wasniewski,Plamen Yalamov Pdf

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 : Valarmathi Sigamani,John J. H. Miller,Shivaranjani Nagarajan,Parthiban Saminathan
Publisher : Springer Nature
Page : 218 pages
File Size : 46,9 Mb
Release : 2022-01-24
Category : Mathematics
ISBN : 9789811675461

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Differential Equations and Applications by Valarmathi Sigamani,John J. H. Miller,Shivaranjani Nagarajan,Parthiban Saminathan Pdf

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.

Author : Hans-Görg Roos,Martin Stynes,Lutz Tobiska
Publisher : Springer Science & Business Media
Page : 364 pages
File Size : 49,9 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9783662032060

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Numerical Methods for Singularly Perturbed Differential Equations by Hans-Görg Roos,Martin Stynes,Lutz Tobiska Pdf

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 : Alexandre L. Madureira
Publisher : Springer
Page : 123 pages
File Size : 54,8 Mb
Release : 2017-02-15
Category : Mathematics
ISBN : 9783319508665

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Numerical Methods and Analysis of Multiscale Problems by Alexandre L. Madureira Pdf

This book is about numerical modeling of multiscale problems, and introduces several asymptotic analysis and numerical techniques which are necessary for a proper approximation of equations that depend on different physical scales. Aimed at advanced undergraduate and graduate students in mathematics, engineering and physics – or researchers seeking a no-nonsense approach –, it discusses examples in their simplest possible settings, removing mathematical hurdles that might hinder a clear understanding of the methods. The problems considered are given by singular perturbed reaction advection diffusion equations in one and two-dimensional domains, partial differential equations in domains with rough boundaries, and equations with oscillatory coefficients. This work shows how asymptotic analysis can be used to develop and analyze models and numerical methods that are robust and work well for a wide range of parameters.

Author : O. Axelsson,L.S. Frank,A. van der Sluis
Publisher : Elsevier
Page : 380 pages
File Size : 41,8 Mb
Release : 2010-07-03
Category : Mathematics
ISBN : 0080871585

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Analytical and Numerical Approaches to Asymptotic Problems in Analysis by O. Axelsson,L.S. Frank,A. van der Sluis Pdf

Analytical and Numerical Approaches to Asymptotic Problems in Analysis

Author : Thomas J. R. Hughes
Publisher : Unknown
Page : 246 pages
File Size : 45,8 Mb
Release : 1979
Category : Mathematics
ISBN : UOM:39015000998396

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Finite Element Methods for Convection Dominated Flows by Thomas J. R. Hughes Pdf

Author : Svetozar D. Margenov,Lubin Georgiev Vulkov,Jerzy Wasniewski
Publisher : Springer
Page : 636 pages
File Size : 55,8 Mb
Release : 2009-02-07
Category : Computers
ISBN : 9783642004643

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Numerical Analysis and Its Applications by Svetozar D. Margenov,Lubin Georgiev Vulkov,Jerzy Wasniewski Pdf

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.