Numerical Time Dependent Partial Differential Equations For Scientists And Engineers


Numerical Time Dependent Partial Differential Equations For Scientists And Engineers
Author: Moysey Brio
Publisher: Academic Press
ISBN: 9780080917047
Size: 66.15 MB
Format: PDF, ePub
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Numerical Time Dependent Partial Differential Equations For Scientists And Engineers

Numerical Time Dependent Partial Differential Equations For Scientists And Engineers by Moysey Brio, Numerical Time Dependent Partial Differential Equations For Scientists And Engineers Books available in PDF, EPUB, Mobi Format. Download Numerical Time Dependent Partial Differential Equations For Scientists And Engineers books, 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
Language: en
Pages: 312
Authors: Moysey Brio, Gary M. Webb, Aramais R. Zakharian
Categories: Mathematics
Type: BOOK - Published: 2010-09-21 - Publisher: Academic Press
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
Numerical Partial Differential Equations for Environmental Scientists and Engineers
Language: en
Pages: 388
Authors: Daniel R. Lynch
Categories: Science
Type: BOOK - Published: 2006-06-02 - Publisher: Springer Science & Business Media
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.
Linear Partial Differential Equations for Scientists and Engineers
Language: en
Pages: 778
Authors: Tyn Myint-U, Lokenath Debnath
Categories: Mathematics
Type: BOOK - Published: 2007-04-05 - Publisher: Springer Science & Business Media
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
Partial Differential Equations with Numerical Methods
Language: en
Pages: 262
Authors: Stig Larsson, Vidar Thomee
Categories: Mathematics
Type: BOOK - Published: 2008-12-05 - Publisher: Springer Science & Business Media
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
Numerical Methods for Engineers and Scientists, Second Edition,
Language: en
Pages: 840
Authors: Joe D. Hoffman, Steven Frankel
Categories: Mathematics
Type: BOOK - Published: 2001-05-31 - Publisher: CRC Press
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
Numerical Methods for Evolutionary Differential Equations
Language: en
Pages: 395
Authors: Uri M. Ascher
Categories: Evolution equations
Type: BOOK - Published: 2008 - Publisher: SIAM
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
Time Dependent Problems and Difference Methods
Language: en
Pages: 642
Authors: Bertil Gustafsson, Heinz-Otto Kreiss, Joseph Oliger
Categories: Mathematics
Type: BOOK - Published: 1995 - Publisher: John Wiley & Sons
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).
Numerical Analysis of Partial Differential Equations
Language: en
Pages: 512
Authors: S. H. Lui, Shaun H. Lui
Categories: Mathematics
Type: BOOK - Published: 2011-08-30 - Publisher: John Wiley & Sons
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
Numerical Solution of Partial Differential Equations by the Finite Element Method
Language: en
Pages: 288
Authors: Claes Johnson
Categories: Mathematics
Type: BOOK - Published: 2012-05-23 - Publisher: Courier Corporation
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
Introduction to Numerical Methods for Time Dependent Differential Equations
Language: en
Pages: 192
Authors: Heinz-Otto Kreiss, Omar Eduardo Ortiz
Categories: Mathematics
Type: BOOK - Published: 2014-04-24 - Publisher: John Wiley & Sons
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