Analysis And Numerics Of Partial Differential Equations

Author : S. H, Lui
Publisher : John Wiley & Sons
Page : 506 pages
File Size : 51,9 Mb
Release : 2012-01-10
Category : Mathematics
ISBN : 9781118111116

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Numerical Analysis of Partial Differential Equations by S. H, Lui Pdf

A balanced guide to the essential techniques for solving elliptic partial differential equations Numerical Analysis of Partial Differential Equations provides a comprehensive, self-contained treatment of the quantitative methods used to solve elliptic partial differential equations (PDEs), with a focus on the efficiency as well as the error of the presented methods. The author utilizes coverage of theoretical PDEs, along with the nu merical solution of linear systems and various examples and exercises, to supply readers with an introduction to the essential concepts in the numerical analysis of PDEs. The book presents the three main discretization methods of elliptic PDEs: finite difference, finite elements, and spectral methods. Each topic has its own devoted chapters and is discussed alongside additional key topics, including: The mathematical theory of elliptic PDEs Numerical linear algebra Time-dependent PDEs Multigrid and domain decomposition PDEs posed on infinite domains The book concludes with a discussion of the methods for nonlinear problems, such as Newton's method, and addresses the importance of hands-on work to facilitate learning. Each chapter concludes with a set of exercises, including theoretical and programming problems, that allows readers to test their understanding of the presented theories and techniques. In addition, the book discusses important nonlinear problems in many fields of science and engineering, providing information as to how they can serve as computing projects across various disciplines. Requiring only a preliminary understanding of analysis, Numerical Analysis of Partial Differential Equations is suitable for courses on numerical PDEs at the upper-undergraduate and graduate levels. The book is also appropriate for students majoring in the mathematical sciences and engineering.

Author : Franco Brezzi,Piero Colli Franzone,Ugo Pietro Gianazza,Gianni Gilardi
Publisher : Springer Science & Business Media
Page : 394 pages
File Size : 40,6 Mb
Release : 2012-12-22
Category : Mathematics
ISBN : 9788847025929

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Analysis and Numerics of Partial Differential Equations by Franco Brezzi,Piero Colli Franzone,Ugo Pietro Gianazza,Gianni Gilardi Pdf

This volume is a selection of contributions offered by friends, collaborators, past students in memory of Enrico Magenes. The first part gives a wide historical perspective of Magenes' work in his 50-year mathematical career; the second part contains original research papers, and shows how ideas, methods, and techniques introduced by Magenes and his collaborators still have an impact on the current research in Mathematics.

Author : Mark S. Gockenbach
Publisher : SIAM
Page : 665 pages
File Size : 55,9 Mb
Release : 2010-12-02
Category : Mathematics
ISBN : 9780898719352

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Partial Differential Equations by Mark S. Gockenbach Pdf

A fresh, forward-looking undergraduate textbook that treats the finite element method and classical Fourier series method with equal emphasis.

Author : Daniel R. Lynch
Publisher : Springer Science & Business Media
Page : 390 pages
File Size : 41,9 Mb
Release : 2006-06-02
Category : Science
ISBN : 9780387236209

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Numerical Partial Differential Equations for Environmental Scientists and Engineers by Daniel R. Lynch Pdf

For readers with some competence in PDE solution properties, this book offers an interdisciplinary approach to problems occurring in natural environmental media: the hydrosphere, atmosphere, cryosphere, lithosphere, biosphere and ionosphere. It presents two major discretization methods: Finite Difference and Finite Element, plus a section on practical approaches to ill-posed problems. The blend of theory, analysis, and implementation practicality supports solving and understanding complicated problems.

Author : Alfio Quarteroni,Alberto Valli
Publisher : Springer Science & Business Media
Page : 551 pages
File Size : 44,7 Mb
Release : 2009-02-11
Category : Mathematics
ISBN : 9783540852681

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Numerical Approximation of Partial Differential Equations by Alfio Quarteroni,Alberto Valli Pdf

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).

Author : Stig Larsson,Vidar Thomee
Publisher : Springer Science & Business Media
Page : 263 pages
File Size : 42,6 Mb
Release : 2008-12-05
Category : Mathematics
ISBN : 9783540887058

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Partial Differential Equations with Numerical Methods by Stig Larsson,Vidar Thomee Pdf

The main theme is the integration of the theory of linear PDE and the theory of finite difference and finite element methods. For each type of PDE, elliptic, parabolic, and hyperbolic, the text contains one chapter on the mathematical theory of the differential equation, followed by one chapter on finite difference methods and one on finite element methods. The chapters on elliptic equations are preceded by a chapter on the two-point boundary value problem for ordinary differential equations. Similarly, the chapters on time-dependent problems are preceded by a chapter on the initial-value problem for ordinary differential equations. There is also one chapter on the elliptic eigenvalue problem and eigenfunction expansion. The presentation does not presume a deep knowledge of mathematical and functional analysis. The required background on linear functional analysis and Sobolev spaces is reviewed in an appendix. The book is suitable for advanced undergraduate and beginning graduate students of applied mathematics and engineering.

Author : J.W. Thomas
Publisher : Springer Science & Business Media
Page : 451 pages
File Size : 53,9 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781489972781

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Numerical Partial Differential Equations: Finite Difference Methods by J.W. Thomas Pdf

What makes this book stand out from the competition is that it is more computational. Once done with both volumes, readers will have the tools to attack a wider variety of problems than those worked out in the competitors' books. The author stresses the use of technology throughout the text, allowing students to utilize it as much as possible.

Author : Peter Knabner,Lutz Angerman
Publisher : Springer Science & Business Media
Page : 426 pages
File Size : 49,6 Mb
Release : 2006-05-26
Category : Mathematics
ISBN : 9780387217628

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Numerical Methods for Elliptic and Parabolic Partial Differential Equations by Peter Knabner,Lutz Angerman Pdf

This text provides an application oriented introduction to the numerical methods for partial differential equations. It covers finite difference, finite element, and finite volume methods, interweaving theory and applications throughout. The book examines modern topics such as adaptive methods, multilevel methods, and methods for convection-dominated problems and includes detailed illustrations and extensive exercises.

Author : Sören Bartels
Publisher : Springer
Page : 393 pages
File Size : 44,7 Mb
Release : 2015-01-19
Category : Mathematics
ISBN : 9783319137971

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Numerical Methods for Nonlinear Partial Differential Equations by Sören Bartels Pdf

The description of many interesting phenomena in science and engineering leads to infinite-dimensional minimization or evolution problems that define nonlinear partial differential equations. While the development and analysis of numerical methods for linear partial differential equations is nearly complete, only few results are available in the case of nonlinear equations. This monograph devises numerical methods for nonlinear model problems arising in the mathematical description of phase transitions, large bending problems, image processing, and inelastic material behavior. For each of these problems the underlying mathematical model is discussed, the essential analytical properties are explained, and the proposed numerical method is rigorously analyzed. The practicality of the algorithms is illustrated by means of short implementations.

Author : Anna Doubova,Manuel González-Burgos,Francisco Guillén-González,Mercedes Marín Beltrán
Publisher : Springer
Page : 249 pages
File Size : 40,9 Mb
Release : 2018-11-02
Category : Mathematics
ISBN : 9783319976136

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Recent Advances in PDEs: Analysis, Numerics and Control by Anna Doubova,Manuel González-Burgos,Francisco Guillén-González,Mercedes Marín Beltrán Pdf

This book contains the main results of the talks given at the workshop “Recent Advances in PDEs: Analysis, Numerics and Control”, which took place in Sevilla (Spain) on January 25-27, 2017. The work comprises 12 contributions given by high-level researchers in the partial differential equation (PDE) area to celebrate the 60th anniversary of Enrique Fernández-Cara (University of Sevilla). The main topics covered here are: Control and inverse problems, Analysis of Fluid mechanics and Numerical Analysis. The work is devoted to researchers in these fields.

Author : Charles A. Hall,Thomas A. Porsching
Publisher : Unknown
Page : 319 pages
File Size : 50,9 Mb
Release : 1990
Category : Mathematics
ISBN : 013626557X

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Numerical Analysis of Partial Differential Equations by Charles A. Hall,Thomas A. Porsching Pdf

Author : Walter A. Strauss
Publisher : John Wiley & Sons
Page : 467 pages
File Size : 51,7 Mb
Release : 2007-12-21
Category : Mathematics
ISBN : 9780470054567

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Partial Differential Equations by Walter A. Strauss Pdf

Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them. It provides the student a broad perspective on the subject, illustrates the incredibly rich variety of phenomena encompassed by it, and imparts a working knowledge of the most important techniques of analysis of the solutions of the equations. In this book mathematical jargon is minimized. Our focus is on the three most classical PDEs: the wave, heat and Laplace equations. Advanced concepts are introduced frequently but with the least possible technicalities. The book is flexibly designed for juniors, seniors or beginning graduate students in science, engineering or mathematics.

Author : William F. Ames
Publisher : Academic Press
Page : 451 pages
File Size : 42,5 Mb
Release : 2014-06-28
Category : Mathematics
ISBN : 9780080571300

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Numerical Methods for Partial Differential Equations by William F. Ames Pdf

This volume is designed as an introduction to the concepts of modern numerical analysis as they apply to partial differential equations. The book contains many practical problems and their solutions, but at the same time, strives to expose the pitfalls--such as overstability, consistency requirements, and the danger of extrapolation to nonlinear problems methods used on linear problems. Numerical Methods for Partial Differential Equations, Third Edition reflects the great accomplishments that have taken place in scientific computation in the fifteen years since the Second Edition was published. This new edition is a drastic revision of the previous one, with new material on boundary elements, spectral methods, the methods of lines, and invariant methods. At the same time, the new edition retains the self-contained nature of the older version, and shares the clarity of its exposition and the integrity of its presentation. Material on finite elements and finite differences have been merged, and now constitute equal partners Additional material has been added on boundary elements, spectral methods, the method of lines, and invariant methods References have been updated, and reflect the additional material Self-contained nature of the Second Edition has been maintained Very suitable for PDE courses

Author : Vitoriano Ruas
Publisher : John Wiley & Sons
Page : 376 pages
File Size : 54,5 Mb
Release : 2016-04-28
Category : Technology & Engineering
ISBN : 9781119111368

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Numerical Methods for Partial Differential Equations by Vitoriano Ruas Pdf

Numerical Methods for Partial Differential Equations: An Introduction Vitoriano Ruas, Sorbonne Universités, UPMC - Université Paris 6, France A comprehensive overview of techniques for the computational solution of PDE's Numerical Methods for Partial Differential Equations: An Introduction covers the three most popular methods for solving partial differential equations: the finite difference method, the finite element method and the finite volume method. The book combines clear descriptions of the three methods, their reliability, and practical implementation aspects. Justifications for why numerical methods for the main classes of PDE's work or not, or how well they work, are supplied and exemplified. Aimed primarily at students of Engineering, Mathematics, Computer Science, Physics and Chemistry among others this book offers a substantial insight into the principles numerical methods in this class of problems are based upon. The book can also be used as a reference for research work on numerical methods for PDE’s. Key features: A balanced emphasis is given to both practical considerations and a rigorous mathematical treatment The reliability analyses for the three methods are carried out in a unified framework and in a structured and visible manner, for the basic types of PDE's Special attention is given to low order methods, as practitioner's overwhelming default options for everyday use New techniques are employed to derive known results, thereby simplifying their proof Supplementary material is available from a companion website.

Author : Zhongqiang Zhang,George Em Karniadakis
Publisher : Springer
Page : 394 pages
File Size : 42,5 Mb
Release : 2017-09-01
Category : Mathematics
ISBN : 9783319575117

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Numerical Methods for Stochastic Partial Differential Equations with White Noise by Zhongqiang Zhang,George Em Karniadakis Pdf

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.