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Computational Methods For Partial Differential Equations
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Book Synopsis Numerical Methods for Partial Differential Equations by : Sandip Mazumder
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
Author :Hans Petter Langtangen Publisher :Springer Science & Business Media ISBN 13 :3662011700 Total Pages :704 pages Book Rating :4.6/5 (62 download)
Book Synopsis Computational Partial Differential Equations by : Hans Petter Langtangen
Download or read book Computational Partial Differential Equations written by Hans Petter Langtangen and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 704 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Numerical Methods for Partial Differential Equations by : Vitoriano Ruas
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.
Book Synopsis Numerical Approximation of Partial Differential Equations by : Alfio Quarteroni
Download or read book Numerical Approximation of Partial Differential Equations written by Alfio Quarteroni and published by Springer Science & Business Media. This book was released on 2009-02-11 with total page 551 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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).
Book Synopsis Computational Partial Differential Equations Using MATLAB by : Jichun Li
Download or read book Computational Partial Differential Equations Using MATLAB written by Jichun Li and published by CRC Press. This book was released on 2008-10-20 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook introduces several major numerical methods for solving various partial differential equations (PDEs) in science and engineering, including elliptic, parabolic, and hyperbolic equations. It covers traditional techniques that include the classic finite difference method and the finite element method as well as state-of-the-art numerical
Book Synopsis Numerical Partial Differential Equations: Finite Difference Methods by : J.W. Thomas
Download or read book Numerical Partial Differential Equations: Finite Difference Methods written by J.W. Thomas and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 451 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Nonlinear Partial Differential Equations in Engineering by : William F. Ames
Download or read book Nonlinear Partial Differential Equations in Engineering written by William F. Ames and published by . This book was released on 1965 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear Partial Differential Equations in Engineering: v. 1.
Book Synopsis Domain Decomposition Methods for the Numerical Solution of Partial Differential Equations by : Tarek Mathew
Download or read book Domain Decomposition Methods for the Numerical Solution of Partial Differential Equations written by Tarek Mathew and published by Springer Science & Business Media. This book was released on 2008-06-25 with total page 775 pages. Available in PDF, EPUB and Kindle. Book excerpt: Domain decomposition methods are divide and conquer computational methods for the parallel solution of partial differential equations of elliptic or parabolic type. The methodology includes iterative algorithms, and techniques for non-matching grid discretizations and heterogeneous approximations. This book serves as a matrix oriented introduction to domain decomposition methodology. A wide range of topics are discussed include hybrid formulations, Schwarz, and many more.
Book Synopsis Numerical Methods for Nonlinear Partial Differential Equations by : Sören Bartels
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.
Book Synopsis Mathematical and Numerical Methods for Partial Differential Equations by : Joël Chaskalovic
Download or read book Mathematical and Numerical Methods for Partial Differential Equations written by Joël Chaskalovic and published by Springer. This book was released on 2014-05-16 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-tutorial offers a concise yet thorough introduction into the mathematical analysis of approximation methods for partial differential equation. A particular emphasis is put on finite element methods. The unique approach first summarizes and outlines the finite-element mathematics in general and then in the second and major part, formulates problem examples that clearly demonstrate the techniques of functional analysis via numerous and diverse exercises. The solutions of the problems are given directly afterwards. Using this approach, the author motivates and encourages the reader to actively acquire the knowledge of finite- element methods instead of passively absorbing the material as in most standard textbooks. This English edition is based on the Finite Element Methods for Engineering Sciences by Joel Chaskalovic.
Book Synopsis Numerical Methods for Differential Equations by : J.R. Dormand
Download or read book Numerical Methods for Differential Equations written by J.R. Dormand and published by CRC Press. This book was released on 1996-02-21 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: With emphasis on modern techniques, Numerical Methods for Differential Equations: A Computational Approach covers the development and application of methods for the numerical solution of ordinary differential equations. Some of the methods are extended to cover partial differential equations. All techniques covered in the text are on a program disk included with the book, and are written in Fortran 90. These programs are ideal for students, researchers, and practitioners because they allow for straightforward application of the numerical methods described in the text. The code is easily modified to solve new systems of equations. Numerical Methods for Differential Equations: A Computational Approach also contains a reliable and inexpensive global error code for those interested in global error estimation. This is a valuable text for students, who will find the derivations of the numerical methods extremely helpful and the programs themselves easy to use. It is also an excellent reference and source of software for researchers and practitioners who need computer solutions to differential equations.
Book Synopsis Computational Partial Differential Equations Using MATLAB® by : Jichun Li
Download or read book Computational Partial Differential Equations Using MATLAB® written by Jichun Li and published by CRC Press. This book was released on 2019-09-26 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this popular text for an Numerical Analysis course, the authors introduce several major methods of solving various partial differential equations (PDEs) including elliptic, parabolic, and hyperbolic equations. It covers traditional techniques including the classic finite difference method, finite element method, and state-of-the-art numercial methods.The text uniquely emphasizes both theoretical numerical analysis and practical implementation of the algorithms in MATLAB. This new edition includes a new chapter, Finite Value Method, the presentation has been tightened, new exercises and applications are included, and the text refers now to the latest release of MATLAB. Key Selling Points: A successful textbook for an undergraduate text on numerical analysis or methods taught in mathematics and computer engineering. This course is taught in every university throughout the world with an engineering department or school. Competitive advantage broader numerical methods (including finite difference, finite element, meshless method, and finite volume method), provides the MATLAB source code for most popular PDEs with detailed explanation about the implementation and theoretical analysis. No other existing textbook in the market offers a good combination of theoretical depth and practical source codes.
Book Synopsis Numerical Treatment of Partial Differential Equations by : Christian Grossmann
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.
Book Synopsis Partial Differential Equations by : Roland Glowinski
Download or read book Partial Differential Equations written by Roland Glowinski and published by Springer Science & Business Media. This book was released on 2008-06-26 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: For more than 250 years partial di?erential equations have been clearly the most important tool available to mankind in order to understand a large variety of phenomena, natural at ?rst and then those originating from - man activity and technological development. Mechanics, physics and their engineering applications were the ?rst to bene?t from the impact of partial di?erential equations on modeling and design, but a little less than a century ago the Schr ̈ odinger equation was the key opening the door to the application of partial di?erential equations to quantum chemistry, for small atomic and molecular systems at ?rst, but then for systems of fast growing complexity. The place of partial di?erential equations in mathematics is a very particular one: initially, the partial di?erential equations modeling natural phenomena were derived by combining calculus with physical reasoning in order to - press conservation laws and principles in partial di?erential equation form, leading to the wave equation, the heat equation, the equations of elasticity, the Euler and Navier–Stokes equations for ?uids, the Maxwell equations of electro-magnetics, etc. It is in order to solve ‘constructively’ the heat equation that Fourier developed the series bearing his name in the early 19th century; Fourier series (and later integrals) have played (and still play) a fundamental roleinbothpureandappliedmathematics,includingmanyareasquiteremote from partial di?erential equations. On the other hand, several areas of mathematics such as di?erential ge- etry have bene?ted from their interactions with partial di?erential equations.
Book Synopsis Fourier Series and Numerical Methods for Partial Differential Equations by : Richard Bernatz
Download or read book Fourier Series and Numerical Methods for Partial Differential Equations written by Richard Bernatz and published by John Wiley & Sons. This book was released on 2010-07-30 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: The importance of partial differential equations (PDEs) in modeling phenomena in engineering as well as in the physical, natural, and social sciences is well known by students and practitioners in these fields. Striking a balance between theory and applications, Fourier Series and Numerical Methods for Partial Differential Equations presents an introduction to the analytical and numerical methods that are essential for working with partial differential equations. Combining methodologies from calculus, introductory linear algebra, and ordinary differential equations (ODEs), the book strengthens and extends readers' knowledge of the power of linear spaces and linear transformations for purposes of understanding and solving a wide range of PDEs. The book begins with an introduction to the general terminology and topics related to PDEs, including the notion of initial and boundary value problems and also various solution techniques. Subsequent chapters explore: The solution process for Sturm-Liouville boundary value ODE problems and a Fourier series representation of the solution of initial boundary value problems in PDEs The concept of completeness, which introduces readers to Hilbert spaces The application of Laplace transforms and Duhamel's theorem to solve time-dependent boundary conditions The finite element method, using finite dimensional subspaces The finite analytic method with applications of the Fourier series methodology to linear version of non-linear PDEs Throughout the book, the author incorporates his own class-tested material, ensuring an accessible and easy-to-follow presentation that helps readers connect presented objectives with relevant applications to their own work. Maple is used throughout to solve many exercises, and a related Web site features Maple worksheets for readers to use when working with the book's one- and multi-dimensional problems. Fourier Series and Numerical Methods for Partial Differential Equations is an ideal book for courses on applied mathematics and partial differential equations at the upper-undergraduate and graduate levels. It is also a reliable resource for researchers and practitioners in the fields of mathematics, science, and engineering who work with mathematical modeling of physical phenomena, including diffusion and wave aspects.
Book Synopsis Numerical Methods for Partial Differential Equations by : William F. Ames
Download or read book Numerical Methods for Partial Differential Equations written by William F. Ames and published by Academic Press. This book was released on 2014-05-10 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical Methods for Partial Differential Equations, Second Edition deals with the use of numerical methods to solve partial differential equations. In addition to numerical fluid mechanics, hopscotch and other explicit-implicit methods are also considered, along with Monte Carlo techniques, lines, fast Fourier transform, and fractional steps methods. Comprised of six chapters, this volume begins with an introduction to numerical calculation, paying particular attention to the classification of equations and physical problems, asymptotics, discrete methods, and dimensionless forms. Subsequent chapters focus on parabolic and hyperbolic equations, elliptic equations, and special topics ranging from singularities and shocks to Navier-Stokes equations and Monte Carlo methods. The final chapter discuss the general concepts of weighted residuals, with emphasis on orthogonal collocation and the Bubnov-Galerkin method. The latter procedure is used to introduce finite elements. This book should be a valuable resource for students and practitioners in the fields of computer science and applied mathematics.
Book Synopsis Numerical Methods for Elliptic and Parabolic Partial Differential Equations by : Peter Knabner
Download or read book Numerical Methods for Elliptic and Parabolic Partial Differential Equations written by Peter Knabner and published by Springer Science & Business Media. This book was released on 2003-06-26 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
