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Numerical Solution of Time Dependent Advection Diffusion Reaction Equations

Numerical Solution of Time Dependent Advection Diffusion Reaction Equations Author Willem Hundsdorfer
ISBN-10 9783662090176
Release 2013-04-17
Pages 472
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Unique book on Reaction-Advection-Diffusion problems

Numerical Methods for Singularly Perturbed Differential Equations

Numerical Methods for Singularly Perturbed Differential Equations Author Hans-G. Roos
ISBN-10 9783662032060
Release 2013-06-29
Pages 352
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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.

Acta Numerica 2010

Acta Numerica 2010 Author Arieh Iserles
ISBN-10 0521192846
Release 2010-05-27
Pages 604
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A high-impact, prestigious, annual publication containing invited surveys by subject leaders: essential reading for all practitioners and researchers.

Advanced Computational Methods in Science and Engineering

Advanced Computational Methods in Science and Engineering Author Barry Koren
ISBN-10 9783642033872
Release 2010-04-29
Pages 498
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The aim of the present book is to show, in a broad and yet deep way, the state of the art in computational science and engineering. Examples of topics addressed are: fast and accurate numerical algorithms, model-order reduction, grid computing, immersed-boundary methods, and specific computational methods for simulating a wide variety of challenging problems, problems such as: fluid-structure interaction, turbulent flames, bone-fracture healing, micro-electro-mechanical systems, failure of composite materials, storm surges, particulate flows, and so on. The main benefit offered to readers of the book is a well-balanced, up-to-date overview over the field of computational science and engineering, through in-depth articles by specialists from the separate disciplines.

Robust Numerical Methods for Singularly Perturbed Differential Equations

Robust Numerical Methods for Singularly Perturbed Differential Equations Author Hans-G. Roos
ISBN-10 9783540344674
Release 2008-09-17
Pages 604
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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 Mathematics and Advanced Applications ENUMATH 2015

Numerical Mathematics and Advanced Applications ENUMATH 2015 Author Bülent Karasözen
ISBN-10 9783319399294
Release 2016-11-09
Pages 643
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The European Conference on Numerical Mathematics and Advanced Applications (ENUMATH), held every 2 years, provides a forum for discussing recent advances in and aspects of numerical mathematics and scientific and industrial applications. The previous ENUMATH meetings took place in Paris (1995), Heidelberg (1997), Jyvaskyla (1999), Ischia (2001), Prague (2003), Santiago de Compostela (2005), Graz (2007), Uppsala (2009), Leicester (2011) and Lausanne (2013). This book presents a selection of invited and contributed lectures from the ENUMATH 2015 conference, which was organised by the Institute of Applied Mathematics (IAM), Middle East Technical University, Ankara, Turkey, from September 14 to 18, 2015. It offers an overview of central recent developments in numerical analysis, computational mathematics, and applications in the form of contributions by leading experts in the field.

Modeling Mesh Generation and Adaptive Numerical Methods for Partial Differential Equations

Modeling  Mesh Generation  and Adaptive Numerical Methods for Partial Differential Equations Author Ivo Babuska
ISBN-10 9781461242482
Release 2012-12-06
Pages 450
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Modeling Mesh Generation and Adaptive Numerical Methods for Partial Differential Equations has been writing in one form or another for most of life. You can find so many inspiration from Modeling Mesh Generation and Adaptive Numerical Methods for Partial Differential Equations also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Modeling Mesh Generation and Adaptive Numerical Methods for Partial Differential Equations book for free.

Numerical Methods for Stochastic Partial Differential Equations with White Noise

Numerical Methods for Stochastic Partial Differential Equations with White Noise Author Zhongqiang Zhang
ISBN-10 9783319575117
Release 2017-09-01
Pages 394
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This book covers numerical methods for stochastic partial differential equations with white noise using the framework of Wong-Zakai approximation. The book begins with some motivational and background material in the introductory chapters and is divided into three parts. Part I covers numerical stochastic ordinary differential equations. Here the authors start with numerical methods for SDEs with delay using the Wong-Zakai approximation and finite difference in time. Part II covers temporal white noise. Here the authors consider SPDEs as PDEs driven by white noise, where discretization of white noise (Brownian motion) leads to PDEs with smooth noise, which can then be treated by numerical methods for PDEs. In this part, recursive algorithms based on Wiener chaos expansion and stochastic collocation methods are presented for linear stochastic advection-diffusion-reaction equations. In addition, stochastic Euler equations are exploited as an application of stochastic collocation methods, where a numerical comparison with other integration methods in random space is made. Part III covers spatial white noise. Here the authors discuss numerical methods for nonlinear elliptic equations as well as other equations with additive noise. Numerical methods for SPDEs with multiplicative noise are also discussed using the Wiener chaos expansion method. In addition, some SPDEs driven by non-Gaussian white noise are discussed and some model reduction methods (based on Wick-Malliavin calculus) are presented for generalized polynomial chaos expansion methods. Powerful techniques are provided for solving stochastic partial differential equations. This book can be considered as self-contained. Necessary background knowledge is presented in the appendices. Basic knowledge of probability theory and stochastic calculus is presented in Appendix A. In Appendix B some semi-analytical methods for SPDEs are presented. In Appendix C an introduction to Gauss quadrature is provided. In Appendix D, all the conclusions which are needed for proofs are presented, and in Appendix E a method to compute the convergence rate empirically is included. In addition, the authors provide a thorough review of the topics, both theoretical and computational exercises in the book with practical discussion of the effectiveness of the methods. Supporting Matlab files are made available to help illustrate some of the concepts further. Bibliographic notes are included at the end of each chapter. This book serves as a reference for graduate students and researchers in the mathematical sciences who would like to understand state-of-the-art numerical methods for stochastic partial differential equations with white noise.

Numerical Approximation of Partial Differential Equations

Numerical Approximation of Partial Differential Equations Author Alfio Quarteroni
ISBN-10 9783540852681
Release 2009-02-11
Pages 544
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Everything is more simple than one thinks but at the same time more complex than one can understand Johann Wolfgang von Goethe To reach the point that is unknown to you, you must take the road that is unknown to you St. John of the Cross This is a book on the numerical approximation ofpartial differential equations (PDEs). Its scope is to provide a thorough illustration of numerical methods (especially those stemming from the variational formulation of PDEs), carry out their stability and convergence analysis, derive error bounds, and discuss the algorithmic aspects relative to their implementation. A sound balancing of theoretical analysis, description of algorithms and discussion of applications is our primary concern. Many kinds of problems are addressed: linear and nonlinear, steady and time-dependent, having either smooth or non-smooth solutions. Besides model equations, we consider a number of (initial-) boundary value problems of interest in several fields of applications. Part I is devoted to the description and analysis of general numerical methods for the discretization of partial differential equations. A comprehensive theory of Galerkin methods and its variants (Petrov Galerkin and generalized Galerkin), as wellas ofcollocationmethods, is devel oped for the spatial discretization. This theory is then specified to two numer ical subspace realizations of remarkable interest: the finite element method (conforming, non-conforming, mixed, hybrid) and the spectral method (Leg endre and Chebyshev expansion).

Computational Fluid Dynamics

Computational Fluid Dynamics Author John Wendt
ISBN-10 9783540850564
Release 2008-10-22
Pages 332
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Computational Fluid Dynamics: An Introduction grew out of a von Karman Institute (VKI) Lecture Series by the same title ?rst presented in 1985 and repeated with modi?cations every year since that time. The objective, then and now, was to present the subject of computational ?uid dynamics (CFD) to an audience unfamiliar with all but the most basic numerical techniques and to do so in such a way that the practical application of CFD would become clear to everyone. A second edition appeared in 1995 with updates to all the chapters and when that printing came to an end, the publisher requested that the editor and authors consider the preparation of a third edition. Happily, the authors received the request with enthusiasm. The third edition has the goal of presenting additional updates and clari?cations while preserving the introductory nature of the material. The book is divided into three parts. John Anderson lays out the subject in Part I by ?rst describing the governing equations of ?uid dynamics, concentrating on their mathematical properties which contain the keys to the choice of the numerical approach. Methods of discretizing the equations are discussed and transformation techniques and grids are presented. Two examples of numerical methods close out this part of the book: source and vortex panel methods and the explicit method. Part II is devoted to four self-contained chapters on more advanced material. Roger Grundmann treats the boundary layer equations and methods of solution.

The Proper Generalized Decomposition for Advanced Numerical Simulations

The Proper Generalized Decomposition for Advanced Numerical Simulations Author Francisco Chinesta
ISBN-10 9783319028651
Release 2013-10-08
Pages 117
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Many problems in scientific computing are intractable with classical numerical techniques. These fail, for example, in the solution of high-dimensional models due to the exponential increase of the number of degrees of freedom. Recently, the authors of this book and their collaborators have developed a novel technique, called Proper Generalized Decomposition (PGD) that has proven to be a significant step forward. The PGD builds by means of a successive enrichment strategy a numerical approximation of the unknown fields in a separated form. Although first introduced and successfully demonstrated in the context of high-dimensional problems, the PGD allows for a completely new approach for addressing more standard problems in science and engineering. Indeed, many challenging problems can be efficiently cast into a multi-dimensional framework, thus opening entirely new solution strategies in the PGD framework. For instance, the material parameters and boundary conditions appearing in a particular mathematical model can be regarded as extra-coordinates of the problem in addition to the usual coordinates such as space and time. In the PGD framework, this enriched model is solved only once to yield a parametric solution that includes all particular solutions for specific values of the parameters. The PGD has now attracted the attention of a large number of research groups worldwide. The present text is the first available book describing the PGD. It provides a very readable and practical introduction that allows the reader to quickly grasp the main features of the method. Throughout the book, the PGD is applied to problems of increasing complexity, and the methodology is illustrated by means of carefully selected numerical examples. Moreover, the reader has free access to the Matlab© software used to generate these examples.

Computational Partial Differential Equations

Computational Partial Differential Equations Author Hans Petter Langtangen
ISBN-10 9783662011706
Release 2013-04-17
Pages 685
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Targeted at students and researchers in computational sciences who need to develop computer codes for solving PDEs, the exposition here is focused on numerics and software related to mathematical models in solid and fluid mechanics. The book teaches finite element methods, and basic finite difference methods from a computational point of view, with the main emphasis on developing flexible computer programs, using the numerical library Diffpack. Diffpack is explained in detail for problems including model equations in applied mathematics, heat transfer, elasticity, and viscous fluid flow. All the program examples, as well as Diffpack for use with this book, are available on the Internet. XXXXXXX NEUER TEXT This book is for researchers who need to develop computer code for solving PDEs. Numerical methods and the application of Diffpack are explained in detail. Diffpack is a modern C++ development environment that is widely used by industrial scientists and engineers working in areas such as oil exploration, groundwater modeling, and materials testing. All the program examples, as well as a test version of Diffpack, are available for free over the Internet.

Flux Corrected Transport

Flux Corrected Transport Author Dmitri Kuzmin
ISBN-10 9789400740389
Release 2012-03-30
Pages 452
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Addressing students and researchers as well as Computational Fluid Dynamics practitioners, this book is the most comprehensive review of high-resolution schemes based on the principle of Flux-Corrected Transport (FCT). The foreword by J.P. Boris and historical note by D.L. Book describe the development of the classical FCT methodology for convection-dominated transport problems, while the design philosophy behind modern FCT schemes is explained by S.T. Zalesak. The subsequent chapters present various improvements and generalizations proposed over the past three decades. In this new edition, recent results are integrated into existing chapters in order to describe significant advances since the publication of the first edition. Also, 3 new chapters were added in order to cover the following topics: algebraic flux correction for finite elements, iterative and linearized FCT schemes, TVD-like flux limiters, acceleration of explicit and implicit solvers, mesh adaptation, failsafe limiting for systems of conservation laws, flux-corrected interpolation (remapping), positivity preservation in RANS turbulence models, and the use of FCT as an implicit subgrid scale model for large eddy simulations.

Spectral Methods

Spectral Methods Author Jie Shen
ISBN-10 9783540710417
Release 2011-08-25
Pages 472
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Along with finite differences and finite elements, spectral methods are one of the three main methodologies for solving partial differential equations on computers. This book provides a detailed presentation of basic spectral algorithms, as well as a systematical presentation of basic convergence theory and error analysis for spectral methods. Readers of this book will be exposed to a unified framework for designing and analyzing spectral algorithms for a variety of problems, including in particular high-order differential equations and problems in unbounded domains. The book contains a large number of figures which are designed to illustrate various concepts stressed in the book. A set of basic matlab codes has been made available online to help the readers to develop their own spectral codes for their specific applications.

Numerical Analysis and Applied Mathematics

Numerical Analysis and Applied Mathematics Author Theodore E. Simos
ISBN-10 073540447X
Release 2007-09-14
Pages 789
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This volume contains peer-reviewed papers presented at the International Conference on Numerical Analysis and Applied Mathematics 2007, ICNAAM-2007. This conference brought together leading scientists of the international Numerical and Applied Mathematics community. More than 350 papers were submitted to be considered for presentation at ICNAAM-2007. From these submissions, 189 papers were selected after an international peer review by at least two independent reviewers.


Newsletter Author New Zealand Mathematical Society
ISBN-10 UOM:39015057376611
Release 2002
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Newsletter has been writing in one form or another for most of life. You can find so many inspiration from Newsletter also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Newsletter book for free.

Computational Fluid Dynamics for Engineers and Scientists

Computational Fluid Dynamics for Engineers and Scientists Author Sreenivas Jayanti
ISBN-10 9789402412178
Release 2018-01-09
Pages 402
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This book offers a practical, application-oriented introduction to computational fluid dynamics (CFD), with a focus on the concepts and principles encountered when using CFD in industry. Presuming no more knowledge than college-level understanding of the core subjects, the book puts together all the necessary topics to give the reader a comprehensive introduction to CFD. It includes discussion of the derivation of equations, grid generation and solution algorithms for compressible, incompressible and hypersonic flows. The final two chapters of the book are intended for the more advanced user. In the penultimate chapter, the special difficulties that arise while solving practical problems are addressed. Distinction is made between complications arising out of geometrical complexity and those arising out of the complexity of the physics (and chemistry) of the problem. The last chapter contains a brief discussion of what can be considered as the Holy Grail of CFD, namely, finding the optimal design of a fluid flow component. A number of problems are given at the end of each chapter to reinforce the concepts and ideas discussed in that chapter. CFD has come of age and is widely used in industry as well as in academia as an analytical tool to investigate a wide range of fluid flow problems. This book is written for two groups: for those students who are encountering CFD for the first time in the form of a taught lecture course, and for those practising engineers and scientists who are already using CFD as an analysis tool in their professions but would like to deepen and broaden their understanding of the subject.