Numerical Solution Of Partial Differential Equations In Science And Engineering

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Numerical Solution of Partial Differential Equations in Science and Engineering

Leon Lapidus,George F. Pinder
Numerical Solution of Partial Differential Equations in Science and Engineering Book PDF

Author : Leon Lapidus,George F. Pinder
Publisher : John Wiley & Sons
Page : 677 pages
File Size : 46,5 Mb
Release : 2011-02-14
Category : Mathematics
ISBN : 9781118031216

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Numerical Solution of Partial Differential Equations in Science and Engineering by Leon Lapidus,George F. Pinder Pdf

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.

Numerical Partial Differential Equations for Environmental Scientists and Engineers

Daniel R. Lynch
Numerical Partial Differential Equations for Environmental Scientists and Engineers Book PDF

Author : Daniel R. Lynch
Publisher : Springer Science & Business Media
Page : 390 pages
File Size : 44,5 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.

Numerical Methods for Solving Partial Differential Equations

George F. Pinder
Numerical Methods for Solving Partial Differential Equations Book PDF

Author : George F. Pinder
Publisher : John Wiley & Sons
Page : 320 pages
File Size : 55,7 Mb
Release : 2018-02-05
Category : Technology & Engineering
ISBN : 9781119316381

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Numerical Methods for Solving Partial Differential Equations by George F. Pinder Pdf

A comprehensive guide to numerical methods for simulating physical-chemical systems This book offers a systematic, highly accessible presentation of numerical methods used to simulate the behavior of physical-chemical systems. Unlike most books on the subject, it focuses on methodology rather than specific applications. Written for students and professionals across an array of scientific and engineering disciplines and with varying levels of experience with applied mathematics, it provides comprehensive descriptions of numerical methods without requiring an advanced mathematical background. Based on its author’s more than forty years of experience teaching numerical methods to engineering students, Numerical Methods for Solving Partial Differential Equations presents the fundamentals of all of the commonly used numerical methods for solving differential equations at a level appropriate for advanced undergraduates and first-year graduate students in science and engineering. Throughout, elementary examples show how numerical methods are used to solve generic versions of equations that arise in many scientific and engineering disciplines. In writing it, the author took pains to ensure that no assumptions were made about the background discipline of the reader. Covers the spectrum of numerical methods that are used to simulate the behavior of physical-chemical systems that occur in science and engineering Written by a professor of engineering with more than forty years of experience teaching numerical methods to engineers Requires only elementary knowledge of differential equations and matrix algebra to master the material Designed to teach students to understand, appreciate and apply the basic mathematics and equations on which Mathcad and similar commercial software packages are based Comprehensive yet accessible to readers with limited mathematical knowledge, Numerical Methods for Solving Partial Differential Equations is an excellent text for advanced undergraduates and first-year graduate students in the sciences and engineering. It is also a valuable working reference for professionals in engineering, physics, chemistry, computer science, and applied mathematics.

Domain Decomposition Methods for the Numerical Solution of Partial Differential Equations

Tarek Mathew
Domain Decomposition Methods for the Numerical Solution of Partial Differential Equations Book PDF

Author : Tarek Mathew
Publisher : Springer Science & Business Media
Page : 775 pages
File Size : 55,8 Mb
Release : 2008-06-25
Category : Mathematics
ISBN : 9783540772095

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Domain Decomposition Methods for the Numerical Solution of Partial Differential Equations by Tarek Mathew Pdf

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.

Numerical Time-Dependent Partial Differential Equations for Scientists and Engineers

Moysey Brio,Gary M. Webb,Aramais R. Zakharian
Numerical Time Dependent Partial Differential Equations for Scientists and Engineers Book PDF

Author : Moysey Brio,Gary M. Webb,Aramais R. Zakharian
Publisher : Academic Press
Page : 312 pages
File Size : 53,5 Mb
Release : 2010-09-21
Category : Mathematics
ISBN : 0080917046

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Numerical Time-Dependent Partial Differential Equations for Scientists and Engineers by Moysey Brio,Gary M. Webb,Aramais R. Zakharian Pdf

It is the first text that in addition to standard convergence theory treats other necessary ingredients for successful numerical simulations of physical systems encountered by every practitioner. The book is aimed at users with interests ranging from application modeling to numerical analysis and scientific software development. It is strongly influenced by the authors research in in space physics, electrical and optical engineering, applied mathematics, numerical analysis and professional software development. The material is based on a year-long graduate course taught at the University of Arizona since 1989. The book covers the first two-semesters of a three semester series. The second semester is based on a semester-long project, while the third semester requirement consists of a particular methods course in specific disciplines like computational fluid dynamics, finite element method in mechanical engineering, computational physics, biology, chemistry, photonics, etc. The first three chapters focus on basic properties of partial differential equations, including analysis of the dispersion relation, symmetries, particular solutions and instabilities of the PDEs; methods of discretization and convergence theory for initial value problems. The goal is to progress from observations of simple numerical artifacts like diffusion, damping, dispersion, and anisotropies to their analysis and management technique, as it is not always possible to completely eliminate them. In the second part of the book we cover topics for which there are only sporadic theoretical results, while they are an integral part and often the most important part for successful numerical simulation. We adopt a more heuristic and practical approach using numerical methods of investigation and validation. The aim is teach students subtle key issues in order to separate physics from numerics. The following topics are addressed: Implementation of transparent and absorbing boundary conditions; Practical stability analysis in the presence of the boundaries and interfaces; Treatment of problems with different temporal/spatial scales either explicit or implicit; preservation of symmetries and additional constraints; physical regularization of singularities; resolution enhancement using adaptive mesh refinement and moving meshes. Self contained presentation of key issues in successful numerical simulation Accessible to scientists and engineers with diverse background Provides analysis of the dispersion relation, symmetries, particular solutions and instabilities of the partial differential equations

Numerical Solution of Partial Differential Equations on Parallel Computers

Are Magnus Bruaset,Aslak Tveito
Numerical Solution of Partial Differential Equations on Parallel Computers Book PDF

Author : Are Magnus Bruaset,Aslak Tveito
Publisher : Springer Science & Business Media
Page : 491 pages
File Size : 54,7 Mb
Release : 2006-03-05
Category : Mathematics
ISBN : 9783540316190

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Numerical Solution of Partial Differential Equations on Parallel Computers by Are Magnus Bruaset,Aslak Tveito Pdf

Since the dawn of computing, the quest for a better understanding of Nature has been a driving force for technological development. Groundbreaking achievements by great scientists have paved the way from the abacus to the supercomputing power of today. When trying to replicate Nature in the computer’s silicon test tube, there is need for precise and computable process descriptions. The scienti?c ?elds of Ma- ematics and Physics provide a powerful vehicle for such descriptions in terms of Partial Differential Equations (PDEs). Formulated as such equations, physical laws can become subject to computational and analytical studies. In the computational setting, the equations can be discreti ed for ef?cient solution on a computer, leading to valuable tools for simulation of natural and man-made processes. Numerical so- tion of PDE-based mathematical models has been an important research topic over centuries, and will remain so for centuries to come. In the context of computer-based simulations, the quality of the computed results is directly connected to the model’s complexity and the number of data points used for the computations. Therefore, computational scientists tend to ?ll even the largest and most powerful computers they can get access to, either by increasing the si e of the data sets, or by introducing new model terms that make the simulations more realistic, or a combination of both. Today, many important simulation problems can not be solved by one single computer, but calls for parallel computing.

Numerical Methods for Partial Differential Equations

Vitoriano Ruas
Numerical Methods for Partial Differential Equations Book PDF

Author : Vitoriano Ruas
Publisher : John Wiley & Sons
Page : 376 pages
File Size : 44,9 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.

Numerical Solution of Partial Differential Equations by the Finite Element Method

Claes Johnson
Numerical Solution of Partial Differential Equations by the Finite Element Method Book PDF

Author : Claes Johnson
Publisher : Courier Corporation
Page : 290 pages
File Size : 49,8 Mb
Release : 2012-05-23
Category : Mathematics
ISBN : 9780486131597

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Numerical Solution of Partial Differential Equations by the Finite Element Method by Claes Johnson Pdf

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 Methods for Differential Equations

Michael Anthony Celia,William Guerin Gray
Numerical Methods for Differential Equations Book PDF

Author : Michael Anthony Celia,William Guerin Gray
Publisher : Unknown
Page : 456 pages
File Size : 46,9 Mb
Release : 1992
Category : Computers
ISBN : UOM:39015049310686

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Numerical Methods for Differential Equations by Michael Anthony Celia,William Guerin Gray Pdf

Senior/Graduate level text covering numerical methods used to solve ordinary and partial differential equations in science and engineering. Emphasis is on problem-solving as a means of gaining a deeper understanding of the fundamental concepts. Not a cookbook of formulas. Topics include an introduction to partial differential equations, finite difference method, finite element approximations, design of numerical approximations, and analytical tools. Includes review of linear algebra.

Numerical Methods for Engineers and Scientists, Second Edition,

Joe D. Hoffman,Steven Frankel
Numerical Methods for Engineers and Scientists Second Edition Book PDF

Author : Joe D. Hoffman,Steven Frankel
Publisher : CRC Press
Page : 842 pages
File Size : 48,7 Mb
Release : 2001-05-31
Category : Mathematics
ISBN : 0824704436

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Numerical Methods for Engineers and Scientists, Second Edition, by Joe D. Hoffman,Steven Frankel Pdf

Emphasizing the finite difference approach for solving differential equations, the second edition of Numerical Methods for Engineers and Scientists presents a methodology for systematically constructing individual computer programs. Providing easy access to accurate solutions to complex scientific and engineering problems, each chapter begins with objectives, a discussion of a representative application, and an outline of special features, summing up with a list of tasks students should be able to complete after reading the chapter- perfect for use as a study guide or for review. The AIAA Journal calls the book "...a good, solid instructional text on the basic tools of numerical analysis."

Linear Partial Differential Equations for Scientists and Engineers

Tyn Myint-U,Lokenath Debnath
Linear Partial Differential Equations for Scientists and Engineers Book PDF

Author : Tyn Myint-U,Lokenath Debnath
Publisher : Springer Science & Business Media
Page : 778 pages
File Size : 50,5 Mb
Release : 2007-04-05
Category : Mathematics
ISBN : 9780817645601

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Linear Partial Differential Equations for Scientists and Engineers by Tyn Myint-U,Lokenath Debnath Pdf

This significantly expanded fourth edition is designed as an introduction to the theory and applications of linear PDEs. The authors provide fundamental concepts, underlying principles, a wide range of applications, and various methods of solutions to PDEs. In addition to essential standard material on the subject, the book contains new material that is not usually covered in similar texts and reference books. It also contains a large number of worked examples and exercises dealing with problems in fluid mechanics, gas dynamics, optics, plasma physics, elasticity, biology, and chemistry; solutions are provided.

PETSc for Partial Differential Equations: Numerical Solutions in C and Python

Ed Bueler
PETSc for Partial Differential Equations Numerical Solutions in C and Python Book PDF

Author : Ed Bueler
Publisher : SIAM
Page : 407 pages
File Size : 53,6 Mb
Release : 2020-10-22
Category : Mathematics
ISBN : 9781611976311

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PETSc for Partial Differential Equations: Numerical Solutions in C and Python by Ed Bueler Pdf

The Portable, Extensible Toolkit for Scientific Computation (PETSc) is an open-source library of advanced data structures and methods for solving linear and nonlinear equations and for managing discretizations. This book uses these modern numerical tools to demonstrate how to solve nonlinear partial differential equations (PDEs) in parallel. It starts from key mathematical concepts, such as Krylov space methods, preconditioning, multigrid, and Newton’s method. In PETSc these components are composed at run time into fast solvers. Discretizations are introduced from the beginning, with an emphasis on finite difference and finite element methodologies. The example C programs of the first 12 chapters, listed on the inside front cover, solve (mostly) elliptic and parabolic PDE problems. Discretization leads to large, sparse, and generally nonlinear systems of algebraic equations. For such problems, mathematical solver concepts are explained and illustrated through the examples, with sufficient context to speed further development. PETSc for Partial Differential Equations addresses both discretizations and fast solvers for PDEs, emphasizing practice more than theory. Well-structured examples lead to run-time choices that result in high solver performance and parallel scalability. The last two chapters build on the reader’s understanding of fast solver concepts when applying the Firedrake Python finite element solver library. This textbook, the first to cover PETSc programming for nonlinear PDEs, provides an on-ramp for graduate students and researchers to a major area of high-performance computing for science and engineering. It is suitable as a supplement for courses in scientific computing or numerical methods for differential equations.

Numerical Methods for Evolutionary Differential Equations

Uri M. Ascher
Numerical Methods for Evolutionary Differential Equations Book PDF

Author : Uri M. Ascher
Publisher : SIAM
Page : 403 pages
File Size : 52,8 Mb
Release : 2008-09-04
Category : Mathematics
ISBN : 9780898716528

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Numerical Methods for Evolutionary Differential Equations by Uri M. Ascher Pdf

Develops, analyses, and applies numerical methods for evolutionary, or time-dependent, differential problems.

Numerical Analysis for Science, Engineering and Technology

Said Gamil Ahmed,Hossein Jafari,Mukhtar Yagoub Youssif,Roberto Datja
Numerical Analysis for Science Engineering and Technology Book PDF

Author : Said Gamil Ahmed,Hossein Jafari,Mukhtar Yagoub Youssif,Roberto Datja
Publisher : Bentham Science Publishers
Page : 280 pages
File Size : 48,7 Mb
Release : 2018-05-02
Category : Mathematics
ISBN : 9781681086514

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Numerical Analysis for Science, Engineering and Technology by Said Gamil Ahmed,Hossein Jafari,Mukhtar Yagoub Youssif,Roberto Datja Pdf

This textbook is intended as a guide for undergraduate and graduate students in engineering, science and technology courses. Chapters of the book cover the numerical concepts of errors, approximations, differential equations and partial differential equations. The simple presentation of numerical concepts and illustrative examples helps students and general readers to understand the topics covered in the text.

Partial Differential Equations for Scientists and Engineers

Stanley J. Farlow
Partial Differential Equations for Scientists and Engineers Book PDF

Author : Stanley J. Farlow
Publisher : Courier Corporation
Page : 414 pages
File Size : 54,7 Mb
Release : 2012-03-08
Category : Mathematics
ISBN : 9780486134734

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Partial Differential Equations for Scientists and Engineers by Stanley J. Farlow Pdf

Practical text shows how to formulate and solve partial differential equations. Coverage of diffusion-type problems, hyperbolic-type problems, elliptic-type problems, numerical and approximate methods. Solution guide available upon request. 1982 edition.