numerical time dependent partial differential equations for scientists and engineers

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Numerical Partial Differential Equations for Environmental Scientists and Engineers
Author : Daniel R. Lynch
Publisher : Springer Science & Business Media
Release Date : 2006-06-02
ISBN 10 : 0387236201
Pages : 388 pages

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 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
ISBN 10 : 9780080917047
Pages : 312 pages

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 by the Finite Element Method
Author : Claes Johnson
Publisher : Courier Corporation
Release Date : 2012-05-23
ISBN 10 : 0486131599
Pages : 288 pages

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.

Linear Partial Differential Equations for Scientists and Engineers
Author : Tyn Myint-U,Lokenath Debnath
Publisher : Springer Science & Business Media
Release Date : 2007-04-05
ISBN 10 : 9780817645601
Pages : 778 pages

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.

Numerical Methods for Evolutionary Differential Equations
Author : Uri M. Ascher
Publisher : SIAM
Release Date : 2008
ISBN 10 : 0898718910
Pages : 395 pages

Methods for the numerical simulation of dynamic mathematical models have been the focus of intensive research for well over 60 years, and the demand for better and more efficient methods has grown as the range of applications has increased. Mathematical models involving evolutionary partial differential equations (PDEs) as well as ordinary differential equations (ODEs) arise in diverse applications such as fluid flow, image processing and computer vision, physics-based animation, mechanical systems, relativity, earth sciences, and mathematical finance. This textbook develops, analyzes, and applies numerical methods for evolutionary, or time-dependent, differential problems. Both PDEs and ODEs are discussed from a unified viewpoint. The author emphasizes finite difference and finite volume methods, specifically their principled derivation, stability, accuracy, efficient implementation, and practical performance in various fields of science and engineering. Smooth and nonsmooth solutions for hyperbolic PDEs, parabolic-type PDEs, and initial value ODEs are treated, and a practical introduction to geometric integration methods is included as well. Audience: suitable for researchers and graduate students from a variety of fields including computer science, applied mathematics, physics, earth and ocean sciences, and various engineering disciplines. Researchers who simulate processes that are modeled by evolutionary differential equations will find material on the principles underlying the appropriate method to use and the pitfalls that accompany each method.

Partial Differential Equations for Scientists and Engineers
Author : Stanley J. Farlow
Publisher : Courier Corporation
Release Date : 2012-03-08
ISBN 10 : 0486134733
Pages : 414 pages

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.

Time Dependent Problems and Difference Methods
Author : Bertil Gustafsson,Heinz-Otto Kreiss,Joseph Oliger
Publisher : John Wiley & Sons
Release Date : 1995
ISBN 10 : 9780471507345
Pages : 642 pages

Time dependent problems frequently pose challenges in areas of science and engineering dealing with numerical analysis, scientific computation, mathematical models, and most importantly--numerical experiments intended to analyze physical behavior and test design. Time Dependent Problems and Difference Methods addresses these various industrial considerations in a pragmatic and detailed manner, giving special attention to time dependent problems in its coverage of the derivation and analysis of numerical methods for computational approximations to Partial Differential Equations (PDEs). The book is written in two parts. Part I discusses problems with periodic solutions; Part II proceeds to discuss initial boundary value problems for partial differential equations and numerical methods for them. The problems with periodic solutions have been chosen because they allow the application of Fourier analysis without the complication that arises from the infinite domain for the corresponding Cauchy problem. Furthermore, the analysis of periodic problems provides necessary conditions when constructing methods for initial boundary value problems. Much of the material included in Part II appears for the first time in this book. The authors draw on their own interests and combined extensive experience in applied mathematics and computer science to bring about this practical and useful guide. They provide complete discussions of the pertinent theorems and back them up with examples and illustrations. For physical scientists, engineers, or anyone who uses numerical experiments to test designs or to predict and investigate physical phenomena, this invaluable guide is destined to become a constant companion. Time Dependent Problems and Difference Methods is also extremely useful to numerical analysts, mathematical modelers, and graduate students of applied mathematics and scientific computations. What Every Physical Scientist and Engineer Needs to Know About Time Dependent Problems . . . Time Dependent Problems and Difference Methods covers the analysis of numerical methods for computing approximate solutions to partial differential equations for time dependent problems. This original book includes for the first time a concrete discussion of initial boundary value problems for partial differential equations. The authors have redone many of these results especially for this volume, including theorems, examples, and over one hundred illustrations. The book takes some less-than-obvious approaches to developing its material: * Treats differential equations and numerical methods with a parallel development, thus achieving a more useful analysis of numerical methods * Covers hyperbolic equations in particularly great detail * Emphasizes error bounds and estimates, as well as the sufficient results needed to justify the methods used for applications Time Dependent Problems and Difference Methods is written for physical scientists and engineers who use numerical experiments to test designs or to predict and investigate physical phenomena. It is also extremely useful to numerical analysts, mathematical modelers, and graduate students of applied mathematics and scientific computations.

Numerical Analysis of Partial Differential Equations
Author : S. H. Lui,Shaun H. Lui
Publisher : John Wiley & Sons
Release Date : 2011-08-30
ISBN 10 : 0470647280
Pages : 512 pages

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 methods. The author utilizes coverage of theoretical PDEs, along with the nu merical solution of linear systems and various examples and exercises, to supply readers with an introduction to the essential concepts in the numerical analysis of PDEs. The book presents the three main discretization methods of elliptic PDEs: finite difference, finite elements, and spectral methods. Each topic has its own devoted chapters and is discussed alongside additional key topics, including: The mathematical theory of elliptic PDEs Numerical linear algebra Time-dependent PDEs Multigrid and domain decomposition PDEs posed on infinite domains The book concludes with a discussion of the methods for nonlinear problems, such as Newton's method, and addresses the importance of hands-on work to facilitate learning. Each chapter concludes with a set of exercises, including theoretical and programming problems, that allows readers to test their understanding of the presented theories and techniques. In addition, the book discusses important nonlinear problems in many fields of science and engineering, providing information as to how they can serve as computing projects across various disciplines. Requiring only a preliminary understanding of analysis, Numerical Analysis of Partial Differential Equations is suitable for courses on numerical PDEs at the upper-undergraduate and graduate levels. The book is also appropriate for students majoring in the mathematical sciences and engineering.

Simulation of ODE/PDE Models with MATLAB®, OCTAVE and SCILAB
Author : Alain Vande Wouwer,Philippe Saucez,Carlos Vilas
Publisher : Springer
Release Date : 2014-06-07
ISBN 10 : 3319067907
Pages : 406 pages

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 This text is suitable for self-study by practicing scientists and engineers and as a final-year undergraduate course or at the graduate level.

Continuum Theory and Modeling of Thermoelectric Elements
Author : Christophe Goupil
Publisher : John Wiley & Sons
Release Date : 2016-02-23
ISBN 10 : 3527413375
Pages : 360 pages

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.

Partial Differential Equations with Numerical Methods
Author : Stig Larsson,Vidar Thomee
Publisher : Springer Science & Business Media
Release Date : 2008-12-05
ISBN 10 : 3540887059
Pages : 262 pages

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.

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
ISBN 10 : 9780821870372
Pages : 194 pages

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.