Download or read book Numerical Treatment of Partial Differential Equations written by Christian Grossmann and published by Springer Science & Business Media. This book was released on 2007-08-11 with total page 601 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with discretization techniques for partial differential equations of elliptic, parabolic and hyperbolic type. It provides an introduction to the main principles of discretization and gives a presentation of the ideas and analysis of advanced numerical methods in the area. The book is mainly dedicated to finite element methods, but it also discusses difference methods and finite volume techniques. Coverage offers analytical tools, properties of discretization techniques and hints to algorithmic aspects. It also guides readers to current developments in research.
Download or read book The Numerical Treatment of Differential Equations written by Lothar Collatz and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: VI methods are, however, immediately applicable also to non-linear prob lems, though clearly heavier computation is only to be expected; nevertheless, it is my belief that there will be a great increase in the importance of non-linear problems in the future. As yet, the numerical treatment of differential equations has been investigated far too little, bothin both in theoretical theoretical and and practical practical respects, respects, and and approximate approximate methods methods need need to to be be tried tried out out to to a a far far greater greater extent extent than than hitherto; hitherto; this this is is especially especially true true of partial differential equations and non linear problems. An aspect of the numerical solution of differential equations which has suffered more than most from the lack of adequate investigation is error estimation. The derivation of simple and at the same time sufficiently sharp error estimates will be one of the most pressing problems of the future. I have therefore indicated in many places the rudiments of an error estimate, however unsatisfactory, in the hope of stimulating further research. Indeed, in this respect the book can only be regarded as an introduction. Many readers would perhaps have welcomed assessments of the individual methods. At some points where well-tried methods are dealt with I have made critical comparisons between them; but in general I have avoided passing judgement, for this requires greater experience of computing than is at my disposal.
Download or read book Numerical Solution of Partial Differential Equations by the Finite Element Method written by Claes Johnson and published by Courier Corporation. This book was released on 2012-05-23 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible introduction to the finite element method for solving numeric problems, this volume offers the keys to an important technique in computational mathematics. Suitable for advanced undergraduate and graduate courses, it outlines clear connections with applications and considers numerous examples from a variety of science- and engineering-related specialties.This text encompasses all varieties of the basic linear partial differential equations, including elliptic, parabolic and hyperbolic problems, as well as stationary and time-dependent problems. Additional topics include finite element methods for integral equations, an introduction to nonlinear problems, and considerations of unique developments of finite element techniques related to parabolic problems, including methods for automatic time step control. The relevant mathematics are expressed in non-technical terms whenever possible, in the interests of keeping the treatment accessible to a majority of students.
Download or read book Elliptic Differential Equations written by W. Hackbusch and published by Springer Science & Business Media. This book was released on 1992 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: Derived from a lecture series for college mathematics students, introduces the methods of dealing with elliptical boundary-value problems--both the theory and the numerical analysis. Includes exercises. Translated and somewhat expanded from the 1987 German version. Annotation copyright by Book News, Inc., Portland, OR
Download or read book Numerical Analysis of Partial Differential Equations written by S. H, Lui and published by John Wiley & Sons. This book was released on 2012-01-10 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Numerical Solution of Partial Differential Equations in Science and Engineering written by Leon Lapidus and published by John Wiley & Sons. This book was released on 2011-02-14 with total page 677 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews of Numerical Solution of PartialDifferential Equations in Science and Engineering: "The book by Lapidus and Pinder is a very comprehensive, evenexhaustive, survey of the subject . . . [It] is unique in that itcovers equally finite difference and finite element methods." Burrelle's "The authors have selected an elementary (but not simplistic)mode of presentation. Many different computational schemes aredescribed in great detail . . . Numerous practical examples andapplications are described from beginning to the end, often withcalculated results given." Mathematics of Computing "This volume . . . devotes its considerable number of pages tolucid developments of the methods [for solving partial differentialequations] . . . the writing is very polished and I found it apleasure to read!" Mathematics of Computation Of related interest . . . NUMERICAL ANALYSIS FOR APPLIED SCIENCE Myron B. Allen andEli L. Isaacson. A modern, practical look at numerical analysis,this book guides readers through a broad selection of numericalmethods, implementation, and basic theoretical results, with anemphasis on methods used in scientific computation involvingdifferential equations. 1997 (0-471-55266-6) 512 pp. APPLIED MATHEMATICS Second Edition, J. David Logan.Presenting an easily accessible treatment of mathematical methodsfor scientists and engineers, this acclaimed work covers fluidmechanics and calculus of variations as well as more modernmethods-dimensional analysis and scaling, nonlinear wavepropagation, bifurcation, and singular perturbation. 1996(0-471-16513-1) 496 pp.
Download or read book Numerical Methods for Partial Differential Equations written by Vitoriano Ruas and published by John Wiley & Sons. This book was released on 2016-04-28 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Numerical Methods for Partial Differential Equations written by Sandip Mazumder and published by Academic Press. This book was released on 2015-12-01 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical Methods for Partial Differential Equations: Finite Difference and Finite Volume Methods focuses on two popular deterministic methods for solving partial differential equations (PDEs), namely finite difference and finite volume methods. The solution of PDEs can be very challenging, depending on the type of equation, the number of independent variables, the boundary, and initial conditions, and other factors. These two methods have been traditionally used to solve problems involving fluid flow. For practical reasons, the finite element method, used more often for solving problems in solid mechanics, and covered extensively in various other texts, has been excluded. The book is intended for beginning graduate students and early career professionals, although advanced undergraduate students may find it equally useful. The material is meant to serve as a prerequisite for students who might go on to take additional courses in computational mechanics, computational fluid dynamics, or computational electromagnetics. The notations, language, and technical jargon used in the book can be easily understood by scientists and engineers who may not have had graduate-level applied mathematics or computer science courses. - Presents one of the few available resources that comprehensively describes and demonstrates the finite volume method for unstructured mesh used frequently by practicing code developers in industry - Includes step-by-step algorithms and code snippets in each chapter that enables the reader to make the transition from equations on the page to working codes - Includes 51 worked out examples that comprehensively demonstrate important mathematical steps, algorithms, and coding practices required to numerically solve PDEs, as well as how to interpret the results from both physical and mathematic perspectives
Download or read book Time dependent Partial Differential Equations and Their Numerical Solution written by Heinz-Otto Kreiss and published by Springer Science & Business Media. This book was released on 2001-04-01 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book studies time-dependent partial differential equations and their numerical solution, developing the analytic and the numerical theory in parallel, and placing special emphasis on the discretization of boundary conditions. The theoretical results are then applied to Newtonian and non-Newtonian flows, two-phase flows and geophysical problems. This book will be a useful introduction to the field for applied mathematicians and graduate students.
Download or read book Numerical Methods for Nonlinear Partial Differential Equations written by Sören Bartels and published by Springer. This book was released on 2015-01-19 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Partial Differential Equations written by J. Necas and published by Routledge. This book was released on 2018-05-04 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: As a satellite conference of the 1998 International Mathematical Congress and part of the celebration of the 650th anniversary of Charles University, the Partial Differential Equations Theory and Numerical Solution conference was held in Prague in August, 1998. With its rich scientific program, the conference provided an opportunity for almost 200 participants to gather and discuss emerging directions and recent developments in partial differential equations (PDEs). This volume comprises the Proceedings of that conference. In it, leading specialists in partial differential equations, calculus of variations, and numerical analysis present up-to-date results, applications, and advances in numerical methods in their fields. Conference organizers chose the contributors to bring together the scientists best able to present a complex view of problems, starting from the modeling, passing through the mathematical treatment, and ending with numerical realization. The applications discussed include fluid dynamics, semiconductor technology, image analysis, motion analysis, and optimal control. The importance and quantity of research carried out around the world in this field makes it imperative for researchers, applied mathematicians, physicists and engineers to keep up with the latest developments. With its panel of international contributors and survey of the recent ramifications of theory, applications, and numerical methods, Partial Differential Equations: Theory and Numerical Solution provides a convenient means to that end.
Download or read book Introduction to Numerical Ordinary and Partial Differential Equations Using MATLAB written by Alexander Stanoyevitch and published by Wiley-Interscience. This book was released on 2005 with total page 868 pages. Available in PDF, EPUB and Kindle. Book excerpt: Learn how to solve complex differential equations using MATLAB® Introduction to Numerical Ordinary and Partial Differential Equations Using MATLAB® teaches readers how to numerically solve both ordinary and partial differential equations with ease. This innovative publication brings together a skillful treatment of MATLAB and programming alongside theory and modeling. By presenting these topics in tandem, the author enables and encourages readers to perform their own computer experiments, leading them to a more profound understanding of differential equations. The text consists of three parts: Introduction to MATLAB and numerical preliminaries, which introduces readers to the software and itsgraphical capabilities and shows how to use it to write programs Ordinary Differential Equations Partial Differential Equations All the tools needed to master using MATLAB to solve differential equations are provided and include: "Exercises for the Reader" that range from routine computations to more advanced conceptual and theoretical questions (solutions appendix included) Illustrative examples, provided throughout the text, that demonstrate MATLAB's powerful ability to solve differential equations Explanations that are rigorous, yet written in a very accessible, user-friendly style Access to an FTP site that includes downloadable files of all the programs developed in the text This textbook can be tailored for courses in numerical differential equations and numerical analysis as well as traditional courses in ordinary and/or partial differential equations. All the material has been classroom-tested over the course of many years, with the result that any self-learner with an understanding of basic single-variable calculus can master this topic. Systematic use is made of MATLAB's superb graphical capabilities to display and analyze results. An extensive chapter on the finite element method covers enough practical aspects (including mesh generation) to enable the reader to numerically solve general elliptic boundary value problems. With its thorough coverage of analytic concepts, geometric concepts, programs and algorithms, and applications, this is an unsurpassed pedagogical tool.
Download or read book Integral Equations written by Wolfgang Hackbusch and published by Birkhäuser. This book was released on 2012-12-06 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of integral equations has been an active research field for many years and is based on analysis, function theory, and functional analysis. On the other hand, integral equations are of practical interest because of the «boundary integral equation method», which transforms partial differential equations on a domain into integral equations over its boundary. This book grew out of a series of lectures given by the author at the Ruhr-Universitat Bochum and the Christian-Albrecht-Universitat zu Kiel to students of mathematics. The contents of the first six chapters correspond to an intensive lecture course of four hours per week for a semester. Readers of the book require background from analysis and the foundations of numeri cal mathematics. Knowledge of functional analysis is helpful, but to begin with some basic facts about Banach and Hilbert spaces are sufficient. The theoretical part of this book is reduced to a minimum; in Chapters 2, 4, and 5 more importance is attached to the numerical treatment of the integral equations than to their theory. Important parts of functional analysis (e. g. , the Riesz-Schauder theory) are presented without proof. We expect the reader either to be already familiar with functional analysis or to become motivated by the practical examples given here to read a book about this topic. We recall that also from a historical point of view, functional analysis was initially stimulated by the investigation of integral equations.
Download or read book Numerical Solution of Differential Equations written by Zhilin Li and published by Cambridge University Press. This book was released on 2017-11-30 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: A practical and concise guide to finite difference and finite element methods. Well-tested MATLAB® codes are available online.
Download or read book Partial Differential Equations written by Walter A. Strauss and published by John Wiley & Sons. This book was released on 2007-12-21 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Numerical PDE Constrained Optimization written by Juan Carlos De los Reyes and published by Springer. This book was released on 2015-02-06 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces, in an accessible way, the basic elements of Numerical PDE-Constrained Optimization, from the derivation of optimality conditions to the design of solution algorithms. Numerical optimization methods in function-spaces and their application to PDE-constrained problems are carefully presented. The developed results are illustrated with several examples, including linear and nonlinear ones. In addition, MATLAB codes, for representative problems, are included. Furthermore, recent results in the emerging field of nonsmooth numerical PDE constrained optimization are also covered. The book provides an overview on the derivation of optimality conditions and on some solution algorithms for problems involving bound constraints, state-constraints, sparse cost functionals and variational inequality constraints.
Download or read book Numerical Solution of Stochastic Differential Equations written by Peter E. Kloeden and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 666 pages. Available in PDF, EPUB and Kindle. Book excerpt: The numerical analysis of stochastic differential equations (SDEs) differs significantly from that of ordinary differential equations. This book provides an easily accessible introduction to SDEs, their applications and the numerical methods to solve such equations. From the reviews: "The authors draw upon their own research and experiences in obviously many disciplines... considerable time has obviously been spent writing this in the simplest language possible." --ZAMP