Numerical Time Dependent Partial Differential Equations for Scientists and Engineers Book

Numerical Time Dependent Partial Differential Equations for Scientists and Engineers


  • Author : Moysey Brio
  • Publisher : Academic Press
  • Release Date : 2010-09-21
  • Genre: Mathematics
  • Pages : 312
  • ISBN 10 : 0080917046

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Numerical Time Dependent Partial Differential Equations for Scientists and Engineers 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

Numerical Partial Differential Equations for Environmental Scientists and Engineers Book

Numerical Partial Differential Equations for Environmental Scientists and Engineers


  • Author : Daniel R. Lynch
  • Publisher : Springer Science & Business Media
  • Release Date : 2006-06-02
  • Genre: Science
  • Pages : 388
  • ISBN 10 : 9780387236209

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Numerical Partial Differential Equations for Environmental Scientists and Engineers Excerpt :

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.

Continuum Theory and Modeling of Thermoelectric Elements Book

Continuum Theory and Modeling of Thermoelectric Elements


  • Author : Christophe Goupil
  • Publisher : John Wiley & Sons
  • Release Date : 2016-02-23
  • Genre: MATHEMATICS
  • Pages : 360
  • ISBN 10 : 9783527413379

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Continuum Theory and Modeling of Thermoelectric Elements Excerpt :

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.

High dimensional Partial Differential Equations in Science and Engineering Book

High dimensional Partial Differential Equations in Science and Engineering


  • Author : André D. Bandrauk
  • Publisher : American Mathematical Soc.
  • Release Date : 2007-01-01
  • Genre: Mathematics
  • Pages : 194
  • ISBN 10 : 0821870378

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High dimensional Partial Differential Equations in Science and Engineering Excerpt :

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 perspectives in many fields of applications. Kinetic plasma physics equations, the many body Schrodinger equation, Dirac and Maxwell equations for molecular electronic structures and nuclear dynamic computations, options pricing equations in mathematical finance, as well as Fokker-Planck and fluid dynamics equations for complex fluids, are examples of equations that can now be handled. The objective of this volume is to bring together contributions by experts of international stature in that broad spectrum of areas to confront their approaches and possibly bring out common problem formulations and research directions in the numerical solutions of high-dimensional partial differential equations in various fields of science and engineering with special emphasis on chemistry and physics. Information for our distributors: Titles in this series are co-published with the Centre de Recherches Mathematiques.

Implementing Spectral Methods for Partial Differential Equations Book
Score: 5
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Implementing Spectral Methods for Partial Differential Equations


  • Author : David A. Kopriva
  • Publisher : Springer Science & Business Media
  • Release Date : 2009-05-27
  • Genre: Mathematics
  • Pages : 397
  • ISBN 10 : 9789048122615

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Implementing Spectral Methods for Partial Differential Equations Excerpt :

This book explains how to solve partial differential equations numerically using single and multidomain spectral methods. It shows how only a few fundamental algorithms form the building blocks of any spectral code, even for problems with complex geometries.

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


  • Author : Claes Johnson
  • Publisher : Courier Corporation
  • Release Date : 2012-05-23
  • Genre: Mathematics
  • Pages : 288
  • ISBN 10 : 9780486131597

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Numerical Solution of Partial Differential Equations by the Finite Element Method 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.

Introduction to Numerical Methods for Time Dependent Differential Equations Book

Introduction to Numerical Methods for Time Dependent Differential Equations


  • Author : Heinz-Otto Kreiss
  • Publisher : John Wiley & Sons
  • Release Date : 2014-04-24
  • Genre: Mathematics
  • Pages : 192
  • ISBN 10 : 9781118838914

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Introduction to Numerical Methods for Time Dependent Differential Equations Excerpt :

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 both ordinary differential equations (ODEs) and partial differential equations (PDEs). Beginning with ODEs and their approximations, the authors provide a crucial presentation of fundamental notions, such as the theory of scalar equations, finite difference approximations, and the Explicit Euler method. Next, a discussion on higher order approximations, implicit methods, multistep methods, Fourier interpolation, PDEs in one space dimension as well as their related systems is provided. Introduction to Numerical Methods for Time Dependent Differential Equations features: A step-by-step discussion of the procedures needed to prove the stability of difference approximations Multiple exercises throughout with select answers, providing readers with a practical guide to understanding the approximations of differential equations A simplified approach in a one space dimension Analytical theory for difference approximations that is particularly useful to clarify procedures Introduction to Numerical Methods for Time Dependent Differential Equations is an excellent textbook for upper-undergraduate courses in applied mathematics, engineering, and physics as well as a useful reference for physical scientists, engineers, numerical analysts, and mathematical modelers who use numerical experiments to test designs or predict and investigate phenomena from many disciplines.

Drying Phenomena Book

Drying Phenomena


  • Author : Ibrahim Dincer
  • Publisher : John Wiley & Sons
  • Release Date : 2016-01-19
  • Genre: Science
  • Pages : 512
  • ISBN 10 : 9781119975861

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Drying Phenomena Excerpt :

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 roles of flow and heat transfer mechanisms on the drying phenomena Considers industrial applications, corresponding criterion, complications, prospects, etc. Discusses novel drying technologies, the corresponding research platforms and potential solutions

Moving Finite Element Method Book

Moving Finite Element Method


  • Author : Maria do Carmo Coimbra
  • Publisher : CRC Press
  • Release Date : 2016-11-30
  • Genre: Mathematics
  • Pages : 248
  • ISBN 10 : 9781498723893

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Moving Finite Element Method Excerpt :

This book focuses on process simulation in chemical engineering with a numerical algorithm based on the moving finite element method (MFEM). It offers new tools and approaches for modeling and simulating time-dependent problems with moving fronts and with moving boundaries described by time-dependent convection-reaction-diffusion partial differential equations in one or two-dimensional space domains. It provides a comprehensive account of the development of the moving finite element method, describing and analyzing the theoretical and practical aspects of the MFEM for models in 1D, 1D+1d, and 2D space domains. Mathematical models are universal, and the book reviews successful applications of MFEM to solve engineering problems. It covers a broad range of application algorithm to engineering problems, namely on separation and reaction processes presenting and discussing relevant numerical applications of the moving finite element method derived from real-world process simulations.

Proper Orthogonal Decomposition Methods for Partial Differential Equations Book

Proper Orthogonal Decomposition Methods for Partial Differential Equations


  • Author : Zhendong Luo
  • Publisher : Academic Press
  • Release Date : 2018-11-26
  • Genre: Mathematics
  • Pages : 278
  • ISBN 10 : 9780128167991

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Proper Orthogonal Decomposition Methods for Partial Differential Equations Excerpt :

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 detailed numerical procedures, implementation and error analysis. Output numerical data are plotted in graphics and compared using standard traditional methods. These models contain parabolic, hyperbolic and nonlinear systems of PDEs, suitable for the user to learn and adapt methods to their own R&D problems. Explains ways to reduce order for PDEs by means of the POD method so that reduced-order models have few unknowns Helps readers speed up computation and reduce computation load and memory requirements while numerically capturing system characteristics Enables readers to apply and adapt the methods to solve similar problems for PDEs of hyperbolic, parabolic and nonlinear types

Handbook of Linear Partial Differential Equations for Engineers and Scientists Book

Handbook of Linear Partial Differential Equations for Engineers and Scientists


  • Author : Andrei D. Polyanin
  • Publisher : CRC Press
  • Release Date : 2015-12-23
  • Genre: Mathematics
  • Pages : 1643
  • ISBN 10 : 9781466581494

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Handbook of Linear Partial Differential Equations for Engineers and Scientists Excerpt :

Includes nearly 4,000 linear partial differential equations (PDEs) with solutionsPresents solutions of numerous problems relevant to heat and mass transfer, wave theory, hydrodynamics, aerodynamics, elasticity, acoustics, electrodynamics, diffraction theory, quantum mechanics, chemical engineering sciences, electrical engineering, and other fieldsO

Simulation of ODE PDE Models with MATLAB    OCTAVE and SCILAB Book

Simulation of ODE PDE Models with MATLAB OCTAVE and SCILAB


  • Author : Alain Vande Wouwer
  • Publisher : Springer
  • Release Date : 2014-06-07
  • Genre: Technology & Engineering
  • Pages : 406
  • ISBN 10 : 9783319067902

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Simulation of ODE PDE Models with MATLAB OCTAVE and SCILAB Excerpt :

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 of algebraic equations, ordinary differential equations (ODEs) and partial differential equations (PDEs). Special attention is paid to the numerical method of lines (MOL), a popular approach to the solution of time-dependent PDEs, which proceeds in two basic steps: spatial discretization and time integration. Besides conventional finite-difference and element techniques, more advanced spatial-approximation methods are examined in some detail, including nonoscillatory schemes and adaptive-grid approaches. A MOL toolbox has been developed within MATLAB®/OCTAVE/SCILAB. In addition to a set of spatial approximations and time integrators, this toolbox includes a collection of application examples, in specific areas, which can serve as templates for developing new programs. Simulation of ODE/PDE Models with MATLAB®, OCTAVE and SCILAB provides a practical introduction to some advanced computational techniques for dynamic system simulation, supported by many worked examples in the text, and a collection of codes available for download from the book’s page at www.springer.com. This text is suitable for self-study by practicing scientists and engineers and as a final-year undergraduate course or at the graduate level.

Time Dependent Problems and Difference Methods Book

Time Dependent Problems and Difference Methods


  • Author : Bertil Gustafsson
  • Publisher : John Wiley & Sons
  • Release Date : 2013-07-18
  • Genre: Mathematics
  • Pages : 528
  • ISBN 10 : 9781118548523

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Time Dependent Problems and Difference Methods Excerpt :

Praise for the First Edition ". . . fills a considerable gap in the numerical analysisliterature by providing a self-contained treatment . . . this is animportant work written in a clear style . . . warmly recommended toany graduate student or researcher in the field of the numericalsolution of partial differential equations." —SIAM Review Time-Dependent Problems and Difference Methods, SecondEdition continues to provide guidance for the analysis ofdifference methods for computing approximate solutions to partialdifferential equations for time-dependent problems. The book treatsdifferential equations and difference methods with a paralleldevelopment, thus achieving a more useful analysis of numericalmethods. The Second Edition presents hyperbolic equations in greatdetail as well as new coverage on second-order systems of waveequations including acoustic waves, elastic waves, and Einsteinequations. Compared to first-order hyperbolic systems,initial-boundary value problems for such systems contain newproperties that must be taken into account when analyzingstability. Featuring the latest material in partial differentialequations with new theorems, examples, andillustrations,Time-Dependent Problems and Difference Methods,Second Edition also includes: High order methods on staggered grids Extended treatment of Summation By Parts operators and theirapplication to second-order derivatives Simplified presentation of certain parts and proofs Time-Dependent Problems and Difference Methods, SecondEdition is an ideal reference for physical scientists,engineers, numerical analysts, and mathematical modelers who usenumerical experiments to test designs and to predict andinvestigate physical phenomena. The book is also excellent forgraduate-level courses in applied mathematics and scientificcomputations.

Numerical Methods and Methods of Approximation in Science and Engineering Book

Numerical Methods and Methods of Approximation in Science and Engineering


  • Author : Karan S. Surana
  • Publisher : CRC Press
  • Release Date : 2018-10-31
  • Genre: Mathematics
  • Pages : 478
  • ISBN 10 : 9780429647864

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Numerical Methods and Methods of Approximation in Science and Engineering Excerpt :

Numerical Methods and Methods of Approximation in Science and Engineering prepares students and other readers for advanced studies involving applied numerical and computational analysis. Focused on building a sound theoretical foundation, it uses a clear and simple approach backed by numerous worked examples to facilitate understanding of numerical methods and their application. Readers will learn to structure a sequence of operations into a program, using the programming language of their choice; this approach leads to a deeper understanding of the methods and their limitations. Features: Provides a strong theoretical foundation for learning and applying numerical methods Takes a generic approach to engineering analysis, rather than using a specific programming language Built around a consistent, understandable model for conducting engineering analysis Prepares students for advanced coursework, and use of tools such as FEA and CFD Presents numerous detailed examples and problems, and a Solutions Manual for instructors

Finite Difference Methods for Ordinary and Partial Differential Equations Book

Finite Difference Methods for Ordinary and Partial Differential Equations


  • Author : Randall J. LeVeque
  • Publisher : SIAM
  • Release Date : 2007-01-01
  • Genre: Mathematics
  • Pages : 356
  • ISBN 10 : 0898717833

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Finite Difference Methods for Ordinary and Partial Differential Equations Excerpt :

This book introduces finite difference methods for both ordinary differential equations (ODEs) and partial differential equations (PDEs) and discusses the similarities and differences between algorithm design and stability analysis for different types of equations. A unified view of stability theory for ODEs and PDEs is presented, and the interplay between ODE and PDE analysis is stressed. The text emphasizes standard classical methods, but several newer approaches also are introduced and are described in the context of simple motivating examples.