Numerical Time Dependent Partial Differential Equations for Scientists and Engineers

Written By Moysey Brio
Numerical Time Dependent Partial Differential Equations for Scientists and Engineers
  • Publsiher : Academic Press
  • Release : 21 September 2010
  • ISBN : 9780080917047
  • Pages : 312 pages
  • Rating : 4/5 from 21 reviews
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Read or download book entitled Numerical Time Dependent Partial Differential Equations for Scientists and Engineers written by Moysey Brio which was release on 21 September 2010, this book published by Academic Press. Available in PDF, EPUB and Kindle Format. Book excerpt: 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 Time Dependent Partial Differential Equations for Scientists and Engineers

Numerical Time Dependent Partial Differential Equations for Scientists and Engineers
  • Author : Moysey Brio,Gary M. Webb,Aramais R. Zakharian
  • Publisher : Academic Press
  • Release Date : 2010-09-21
  • Total pages : 312
  • ISBN : 9780080917047
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Summary : 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 ...

Proper Orthogonal Decomposition Methods for Partial Differential Equations

Proper Orthogonal Decomposition Methods for Partial Differential Equations
  • Author : Zhendong Luo,Goong Chen
  • Publisher : Academic Press
  • Release Date : 2018-11-26
  • Total pages : 278
  • ISBN : 9780080917047
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Summary : Proper Orthogonal Decomposition Methods for Partial Differential Equations evaluates the potential applications of POD reduced-order numerical methods in increasing computational efficiency, decreasing calculating load and alleviating the accumulation of truncation error in the computational process. Introduces the foundations of finite-differences, finite-elements and finite-volume-elements. Models of time-dependent PDEs are presented, with ...

Continuum Theory and Modeling of Thermoelectric Elements

Continuum Theory and Modeling of Thermoelectric Elements
  • Author : Christophe Goupil
  • Publisher : John Wiley & Sons
  • Release Date : 2016-02-23
  • Total pages : 360
  • ISBN : 9780080917047
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Summary : This volume presents the latest research results in the thermodynamics and design of thermoelectric devices, providing a solid foundation for thermoelectric element and module design in the technical development process, and a valuable tool for any application development....

Introduction to Numerical Methods for Time Dependent Differential Equations

Introduction to Numerical Methods for Time Dependent Differential Equations
  • Author : Heinz-Otto Kreiss,Omar Eduardo Ortiz
  • Publisher : John Wiley & Sons
  • Release Date : 2014-04-24
  • Total pages : 192
  • ISBN : 9780080917047
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Summary : Introduces both the fundamentals of time dependent differential equations and their numerical solutions Introduction to Numerical Methods for Time Dependent Differential Equations delves into the underlying mathematical theory needed to solve time dependent differential equations numerically. Written as a self-contained introduction, the book is divided into two parts to emphasize ...

Solving Partial Differential Equation Applications with PDE2D

Solving Partial Differential Equation Applications with PDE2D
  • Author : Granville Sewell
  • Publisher : John Wiley & Sons
  • Release Date : 2018-09-06
  • Total pages : 224
  • ISBN : 9780080917047
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Summary : Solve engineering and scientific partial differential equation applications using the PDE2D software developed by the author Solving Partial Differential Equation Applications with PDE2D derives and solves a range of ordinary and partial differential equation (PDE) applications. This book describes an easy-to-use, general purpose, and time-tested PDE solver developed ...

Geometric Partial Differential Equations Part I

Geometric Partial Differential Equations   Part I
  • Author : Anonim
  • Publisher : Elsevier
  • Release Date : 2020-01-14
  • Total pages : 710
  • ISBN : 9780080917047
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Summary : Besides their intrinsic mathematical interest, geometric partial differential equations (PDEs) are ubiquitous in many scientific, engineering and industrial applications. They represent an intellectual challenge and have received a great deal of attention recently. The purpose of this volume is to provide a missing reference consisting of self-contained and comprehensive presentations. ...

Numerical Solution of Partial Differential Equations in Science and Engineering

Numerical Solution of Partial Differential Equations in Science and Engineering
  • Author : Leon Lapidus,George F. Pinder
  • Publisher : John Wiley & Sons
  • Release Date : 2011-02-14
  • Total pages : 677
  • ISBN : 9780080917047
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Summary : 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 ...

Numerical methods for scientists and engineers

Numerical methods for scientists and engineers
  • Author : H. M. Antia
  • Publisher : Springer
  • Release Date : 2012-11-15
  • Total pages : 888
  • ISBN : 9780080917047
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Summary : This book presents an exhaustive and in-depth exposition of the various numerical methods used in scientific and engineering computations. It emphasises the practical aspects of numerical computation and discusses various techniques in sufficient detail to enable their implementation in solving a wide range of problems. The main addition in the ...

High dimensional Partial Differential Equations in Science and Engineering

High dimensional Partial Differential Equations in Science and Engineering
  • Author : André D. Bandrauk,Michel C. Delfour,Claude Le Bris
  • Publisher : American Mathematical Soc.
  • Release Date : 2007-01-01
  • Total pages : 194
  • ISBN : 9780080917047
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Summary : High-dimensional spatio-temporal partial differential equations are a major challenge to scientific computing of the future. Up to now deemed prohibitive, they have recently become manageable by combining recent developments in numerical techniques, appropriate computer implementations, and the use of computers with parallel and even massively parallel architectures. This opens new ...

Geometric Partial Differential Equations Part 2

Geometric Partial Differential Equations   Part 2
  • Author : Andrea Bonito,Ricardo Horacio Nochetto
  • Publisher : Elsevier
  • Release Date : 2021-01-26
  • Total pages : 570
  • ISBN : 9780080917047
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Summary : Besides their intrinsic mathematical interest, geometric partial differential equations (PDEs) are ubiquitous in many scientific, engineering and industrial applications. They represent an intellectual challenge and have received a great deal of attention recently. The purpose of this volume is to provide a missing reference consisting of self-contained and comprehensive presentations. ...

Simulation of ODE PDE Models with MATLAB OCTAVE and SCILAB

Simulation of ODE PDE Models with MATLAB    OCTAVE and SCILAB
  • Author : Alain Vande Wouwer,Philippe Saucez,Carlos Vilas Fernández
  • Publisher : Springer
  • Release Date : 2014-07-01
  • Total pages : 406
  • ISBN : 9780080917047
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Summary : Simulation of ODE/PDE Models with MATLAB®, OCTAVE and SCILAB shows the reader how to exploit a fuller array of numerical methods for the analysis of complex scientific and engineering systems than is conventionally employed. The book is dedicated to numerical simulation of distributed parameter systems described by mixed systems ...

Simulation of ODE PDE Models with MATLAB OCTAVE and SCILAB

Simulation of ODE PDE Models with MATLAB    OCTAVE and SCILAB
  • Author : Alain Vande Wouwer,Philippe Saucez,Carlos Vilas
  • Publisher : Springer
  • Release Date : 2017-04-30
  • Total pages : 406
  • ISBN : 9780080917047
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Summary : Simulation of ODE/PDE Models with MATLAB®, OCTAVE and SCILAB shows the reader how to exploit a fuller array of numerical methods for the analysis of complex scientific and engineering systems than is conventionally employed. The book is dedicated to numerical simulation of distributed parameter systems described by mixed systems ...

Numerical Partial Differential Equations for Environmental Scientists and Engineers

Numerical Partial Differential Equations for Environmental Scientists and Engineers
  • Author : Daniel R. Lynch
  • Publisher : Springer Science & Business Media
  • Release Date : 2006-06-02
  • Total pages : 388
  • ISBN : 9780080917047
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Summary : 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. ...

Numerical Analysis of Partial Differential Equations

Numerical Analysis of Partial Differential Equations
  • Author : S. H, Lui
  • Publisher : John Wiley & Sons
  • Release Date : 2012-01-10
  • Total pages : 512
  • ISBN : 9780080917047
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Summary : 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 ...

Drying Phenomena

Drying Phenomena
  • Author : Ibrahim Dincer,Calin Zamfirescu
  • Publisher : John Wiley & Sons
  • Release Date : 2015-10-14
  • Total pages : 512
  • ISBN : 9780080917047
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Summary : Comprehensively covers conventional and novel drying systems and applications, while keeping a focus on the fundamentals of drying phenomena. Presents detailed thermodynamic and heat/mass transfer analyses in a reader-friendly and easy-to-follow approach Includes case studies, illustrative examples and problems Presents experimental and computational approaches Includes comprehensive information identifying the ...