Numerical Solution Of Partial Differential Equations By The Finite Element Method
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Numerical Solution Of Partial Differential Equations By The Finite Element Method
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Author : Claes Johnson
language : en
Publisher: Courier Corporation
Release Date : 2012-05-23
Numerical Solution Of Partial Differential Equations By The Finite Element Method written by Claes Johnson and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-23 with Mathematics categories.
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.
Numerical Solution Of Partial Differential Equations Using The Finite Element Method
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Author : Wieland Richter
language : en
Publisher:
Release Date : 1990
Numerical Solution Of Partial Differential Equations Using The Finite Element Method written by Wieland Richter and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Differential equations, Partial categories.
Numerical Solution Of Partial Differential Equations In Science And Engineering
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Author : Leon Lapidus
language : en
Publisher: John Wiley & Sons
Release Date : 2011-02-14
Numerical Solution Of Partial Differential Equations In Science And Engineering written by Leon Lapidus and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-02-14 with Mathematics categories.
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.
Partial Differential Equations And The Finite Element Method
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Author : Pavel Ŝolín
language : en
Publisher: John Wiley & Sons
Release Date : 2005-12-16
Partial Differential Equations And The Finite Element Method written by Pavel Ŝolín and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-12-16 with Mathematics categories.
A systematic introduction to partial differential equations and modern finite element methods for their efficientnumerical solution Partial Differential Equations and the Finite Element Methodprovides a much-needed, clear, and systematic introduction tomodern theory of partial differential equations (PDEs) and finiteelement methods (FEM). Both nodal and hierachic concepts of the FEMare examined. Reflecting the growing complexity and multiscalenature of current engineering and scientific problems, the authoremphasizes higher-order finite element methods such as the spectralor hp-FEM. A solid introduction to the theory of PDEs and FEM contained inChapters 1-4 serves as the core and foundation of the publication.Chapter 5 is devoted to modern higher-order methods for thenumerical solution of ordinary differential equations (ODEs) thatarise in the semidiscretization of time-dependent PDEs by theMethod of Lines (MOL). Chapter 6 discusses fourth-order PDEs rootedin the bending of elastic beams and plates and approximates theirsolution by means of higher-order Hermite and Argyris elements.Finally, Chapter 7 introduces the reader to various PDEs governingcomputational electromagnetics and describes their finite elementapproximation, including modern higher-order edge elements forMaxwell's equations. The understanding of many theoretical and practical aspects of bothPDEs and FEM requires a solid knowledge of linear algebra andelementary functional analysis, such as functions and linearoperators in the Lebesgue, Hilbert, and Sobolev spaces. Thesetopics are discussed with the help of many illustrative examples inAppendix A, which is provided as a service for those readers whoneed to gain the necessary background or require a refreshertutorial. Appendix B presents several finite element computationsrooted in practical engineering problems and demonstrates thebenefits of using higher-order FEM. Numerous finite element algorithms are written out in detailalongside implementation discussions. Exercises, including manythat involve programming the FEM, are designed to assist the readerin solving typical problems in engineering and science. Specifically designed as a coursebook, this student-testedpublication is geared to upper-level undergraduates and graduatestudents in all disciplines of computational engineeringandscience. It is also a practical problem-solving reference forresearchers, engineers, and physicists.
The Numerical Solution Of Ordinary And Partial Differential Equations
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Author : Granville Sewell
language : en
Publisher: World Scientific
Release Date : 2014-12-16
The Numerical Solution Of Ordinary And Partial Differential Equations written by Granville Sewell and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-16 with Mathematics categories.
This book presents methods for the computational solution of differential equations, both ordinary and partial, time-dependent and steady-state. Finite difference methods are introduced and analyzed in the first four chapters, and finite element methods are studied in chapter five. A very general-purpose and widely-used finite element program, PDE2D, which implements many of the methods studied in the earlier chapters, is presented and documented in Appendix A. The book contains the relevant theory and error analysis for most of the methods studied, but also emphasizes the practical aspects involved in implementing the methods. Students using this book will actually see and write programs (FORTRAN or MATLAB) for solving ordinary and partial differential equations, using both finite differences and finite elements. In addition, they will be able to solve very difficult partial differential equations using the software PDE2D, presented in Appendix A. PDE2D solves very general steady-state, time-dependent and eigenvalue PDE systems, in 1D intervals, general 2D regions, and a wide range of simple 3D regions. Contents:Direct Solution of Linear SystemsInitial Value Ordinary Differential EquationsThe Initial Value Diffusion ProblemThe Initial Value Transport and Wave ProblemsBoundary Value ProblemsThe Finite Element MethodsAppendix A — Solving PDEs with PDE2DAppendix B — The Fourier Stability MethodAppendix C — MATLAB ProgramsAppendix D — Answers to Selected Exercises Readership: Undergraduate, graduate students and researchers. Key Features:The discussion of stability, absolute stability and stiffness in Chapter 1 is clearer than in other textsStudents will actually learn to write programs solving a range of simple PDEs using the finite element method in chapter 5In Appendix A, students will be able to solve quite difficult PDEs, using the author's software package, PDE2D. (a free version is available which solves small to moderate sized problems)Keywords:Differential Equations;Partial Differential Equations;Finite Element Method;Finite Difference Method;Computational Science;Numerical AnalysisReviews: "This book is very well written and it is relatively easy to read. The presentation is clear and straightforward but quite rigorous. This book is suitable for a course on the numerical solution of ODEs and PDEs problems, designed for senior level undergraduate or beginning level graduate students. The numerical techniques for solving problems presented in the book may also be useful for experienced researchers and practitioners both from universities or industry." Andrzej Icha Pomeranian Academy in Słupsk Poland
Numerical Solution Of Partial Differential Equations
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Author : Gordon D. Smith
language : en
Publisher: Oxford University Press
Release Date : 1985
Numerical Solution Of Partial Differential Equations written by Gordon D. Smith and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with Computers categories.
Substantially revised, this authoritative study covers the standard finite difference methods of parabolic, hyperbolic, and elliptic equations, and includes the concomitant theoretical work on consistency, stability, and convergence. The new edition includes revised and greatly expanded sections on stability based on the Lax-Richtmeyer definition, the application of Pade approximants to systems of ordinary differential equations for parabolic and hyperbolic equations, and a considerably improved presentation of iterative methods. A fast-paced introduction to numerical methods, this will be a useful volume for students of mathematics and engineering, and for postgraduates and professionals who need a clear, concise grounding in this discipline.
A Survey Of Numerical Methods For Partial Differential Equations
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Author : I. Gladwell
language : en
Publisher: Oxford University Press, USA
Release Date : 1979
A Survey Of Numerical Methods For Partial Differential Equations written by I. Gladwell and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with Differential equations, Partial categories.
Partial Differential Equations With Numerical Methods
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Author : Stig Larsson
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-12-05
Partial Differential Equations With Numerical Methods written by Stig Larsson and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-12-05 with Mathematics categories.
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.
Numerical Methods For Partial Differential Equations
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Author : Sandip Mazumder
language : en
Publisher: Academic Press
Release Date : 2015-12-01
Numerical Methods For Partial Differential Equations written by Sandip Mazumder and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-01 with Technology & Engineering categories.
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
The Numerical Solution Of Ordinary And Partial Differential Equations
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Author : Granville Sewell
language : en
Publisher: John Wiley & Sons
Release Date : 2005-07-25
The Numerical Solution Of Ordinary And Partial Differential Equations written by Granville Sewell and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-07-25 with Mathematics categories.
Learn to write programs to solve ordinary and partial differential equations The Second Edition of this popular text provides an insightful introduction to the use of finite difference and finite element methods for the computational solution of ordinary and partial differential equations. Readers gain a thorough understanding of the theory underlying themethods presented in the text. The author emphasizes the practical steps involved in implementing the methods, culminating in readers learning how to write programs using FORTRAN90 and MATLAB(r) to solve ordinary and partial differential equations. The book begins with a review of direct methods for the solution of linear systems, with an emphasis on the special features of the linear systems that arise when differential equations are solved. The following four chapters introduce and analyze the more commonly used finite difference methods for solving a variety of problems, including ordinary and partial differential equations and initial value and boundary value problems. The techniques presented in these chapters, with the aid of carefully developed exercises and numerical examples, can be easilymastered by readers. The final chapter of the text presents the basic theory underlying the finite element method. Following the guidance offered in this chapter, readers gain a solid understanding of the method and discover how to use it to solve many problems. A special feature of the Second Edition is Appendix A, which describes a finite element program, PDE2D, developed by the author. Readers discover how PDE2D can be used to solve difficult partial differential equation problems, including nonlinear time-dependent and steady-state systems, and linear eigenvalue systems in 1D intervals, general 2D regions, and a wide range of simple 3D regions. The software itself is available to instructors who adopt the text to share with their students.